Question
Define the measures of angles opposite to equal sides in a triangle?
- Are equal in measure
- One is double the other
- One is half the other
- Both the angles are complementary
Hint:
The measures of angles opposite to equal sides in a triangle are equal in measure
The correct answer is: Are equal in measure
The measures of angles opposite to equal sides in a triangle are equal in measure
Related Questions to study
What is the measure of each angle of an equilateral triangle?
What is the measure of each angle of an equilateral triangle?
In which triangle all three sides are of equal measure?
In which triangle all three sides are of equal measure?
Find the vertices of each of the figures of rotation 900 counter-clockwise about the origin
Given Data:
>>From figure, the vertices of the triangle are:
B(-5,0) and E(-2,1) and G(-2, -3).
>>>let, the point (x, y) be in the space and the Angle of Rotation becomes 
= 90.
>>>new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 -y sin90 , y cos90 + x sin90)
= (-y, x).
* Hence, the final coordinates after rotation through 90 degrees counter clockwise are (-y, x).
>>>Similarly, for the coordinates B(-5,0) and E(-2,1) and G(-2, -3) the rotation of points through 90 degrees counter clock wise becomes:
B(0,-5) and E(3, -2) and G(3,2).
***Therefore, the coordinates of triangle B(-5,0) and E(-2,1) and G(-2, -3) after rotation through 90 degrees counter clockwise becomes B(0,-5) and E(3, -2) and G(3,2).
Find the vertices of each of the figures of rotation 900 counter-clockwise about the origin
Given Data:
>>From figure, the vertices of the triangle are:
B(-5,0) and E(-2,1) and G(-2, -3).
>>>let, the point (x, y) be in the space and the Angle of Rotation becomes = 90.
>>>new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 -y sin90 , y cos90 + x sin90)
= (-y, x).
* Hence, the final coordinates after rotation through 90 degrees counter clockwise are (-y, x).
>>>Similarly, for the coordinates B(-5,0) and E(-2,1) and G(-2, -3) the rotation of points through 90 degrees counter clock wise becomes:
B(0,-5) and E(3, -2) and G(3,2).
***Therefore, the coordinates of triangle B(-5,0) and E(-2,1) and G(-2, -3) after rotation through 90 degrees counter clockwise becomes B(0,-5) and E(3, -2) and G(3,2).
Find the vertices of each of the figure of rotation 900 clockwise about the origin
Given Data:
* From figure, the points are K(2, -2) and U(3, 3) and T(5, 0) are the vertices of the triangle.
>>Let (x, y) be the point in the space and angle of rotation becomes = -90 degrees.
*Then, the new coordinates are :
= (x cos - y sin , y cos + x sin)
= (x cos(-90) -y sin(-90) , y cos(-90) + x sin(-90))
= (y, -x).
>>Then, the new coordinates are (y, -x).
>>>Similarly, the rotation of triangular vertices K(2, -2) and U(3, 3) and T(5, 0) through 90 degrees clockwise becomes :
K(-2, -2) and U(3, -3) and T(0, -5).
*Therefore, the vertices K(2, -2) and U(3, 3) and T(5, 0) after rotation through 90 degrees clockwise becomes K(-2, -2) and U(3, -3) and T(0, -5).
Find the vertices of each of the figure of rotation 900 clockwise about the origin
Given Data:
* From figure, the points are K(2, -2) and U(3, 3) and T(5, 0) are the vertices of the triangle.
>>Let (x, y) be the point in the space and angle of rotation becomes = -90 degrees.
*Then, the new coordinates are :
= (x cos - y sin , y cos + x sin)
= (x cos(-90) -y sin(-90) , y cos(-90) + x sin(-90))
= (y, -x).
>>Then, the new coordinates are (y, -x).
>>>Similarly, the rotation of triangular vertices K(2, -2) and U(3, 3) and T(5, 0) through 90 degrees clockwise becomes :
K(-2, -2) and U(3, -3) and T(0, -5).
*Therefore, the vertices K(2, -2) and U(3, 3) and T(5, 0) after rotation through 90 degrees clockwise becomes K(-2, -2) and U(3, -3) and T(0, -5).
Find the vertices of each of the figure of rotation 1800 about the origin
Given Data:
>>From figure, the coordinates of the points w, u, x are.
>>> W(-4, -3) and U(4, 0) and X(-3, -2) are the required coordinates of a triangle.
>>Let, (x, y) be the point in the space and are rotated through 180 degrees.
Then, the new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos180 -y sin180 , y cos180 + xsin180)
= (-x , -y)
* Then, the new coordinates of (x, y) after rotation through 180 degrees is (-x, -y).
>>>Similarly, for W(-4, -3) and U(4, 0) and X(-3, -2) the new coordinates are:
W(4, 3) and U(-4, 0) and (3, 2).
>>>Hence, the rotation of points W(-4, -3) and U(4, 0) and X(-3, -2) through 180 degrees becomes W(4, 3) and U(-4, 0) and (3, 2).
Find the vertices of each of the figure of rotation 1800 about the origin
Given Data:
>>From figure, the coordinates of the points w, u, x are.
>>> W(-4, -3) and U(4, 0) and X(-3, -2) are the required coordinates of a triangle.
>>Let, (x, y) be the point in the space and are rotated through 180 degrees.
Then, the new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos180 -y sin180 , y cos180 + xsin180)
= (-x , -y)
* Then, the new coordinates of (x, y) after rotation through 180 degrees is (-x, -y).
>>>Similarly, for W(-4, -3) and U(4, 0) and X(-3, -2) the new coordinates are:
W(4, 3) and U(-4, 0) and (3, 2).
>>>Hence, the rotation of points W(-4, -3) and U(4, 0) and X(-3, -2) through 180 degrees becomes W(4, 3) and U(-4, 0) and (3, 2).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 90o counter-clockwise about the origin?
Given That:
A (-3,4) B (0, 1), C (-5, 2) are the vertices of a triangle.
>>>The vertices of a triangle are rotated through 90 degrees counter clockwise direction.
>>>Let, the point on the space be (x, y). Then Angle of Rotation becomes 90 degrees.
>>>Hence, new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 - y sin90 , y cos90 + x sin90)
= (-y , x).
>>>Similarly, the rotation of the points A (-3,4) B (0, 1), C (-5, 2) becomes:
A(-4,-3) and B(-1,0) and C(-2, -5).
***Therefore, the triangle vertices A (-3,4) B (0, 1), C (-5, 2) after rotation through 90 degrees counter clockwise are A(-4,-3) and B(-1,0) and C(-2, -5).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 90o counter-clockwise about the origin?
Given That:
A (-3,4) B (0, 1), C (-5, 2) are the vertices of a triangle.
>>>The vertices of a triangle are rotated through 90 degrees counter clockwise direction.
>>>Let, the point on the space be (x, y). Then Angle of Rotation becomes 90 degrees.
>>>Hence, new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos90 - y sin90 , y cos90 + x sin90)
= (-y , x).
>>>Similarly, the rotation of the points A (-3,4) B (0, 1), C (-5, 2) becomes:
A(-4,-3) and B(-1,0) and C(-2, -5).
***Therefore, the triangle vertices A (-3,4) B (0, 1), C (-5, 2) after rotation through 90 degrees counter clockwise are A(-4,-3) and B(-1,0) and C(-2, -5).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 180o about the origin?
Given That:
A (-3,4), B(0, 1), C (-5, 2) are the points of triangle.
>>we re asked to rotate the vertices of triangle by 180 degrees.
>>>let, the point be (x, y) then the angle of rotation be 180 degrees. Then:
>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (x cos180 - y sin180 , y cos180 + x sin180)
= (-x , -y).
>>>Hence, any point that rotated by 180 degrees will just change the sign of the coordinates.
>>>Similarly, for triangle coordinates A (-3,4), B(0, 1), C (-5, 2) the rotation through 180 degrees about origin becomes : A(3, -4) and B(0, -1) and C(5, -2).
What will be the coordinates of the image of ABC with points A (-3,4) B (0, 1), C (-5, 2) after it is rotated 180o about the origin?
Given That:
A (-3,4), B(0, 1), C (-5, 2) are the points of triangle.
>>we re asked to rotate the vertices of triangle by 180 degrees.
>>>let, the point be (x, y) then the angle of rotation be 180 degrees. Then:
>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (x cos180 - y sin180 , y cos180 + x sin180)
= (-x , -y).
>>>Hence, any point that rotated by 180 degrees will just change the sign of the coordinates.
>>>Similarly, for triangle coordinates A (-3,4), B(0, 1), C (-5, 2) the rotation through 180 degrees about origin becomes : A(3, -4) and B(0, -1) and C(5, -2).
In what quadrant will an image be if the figure is in quadrant I and is rotated 90° counter clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
In what quadrant will an image be if the figure is in quadrant I and is rotated 90° counter clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
In what quadrant will an image be if the figure is in quadrant II and is rotated 180° clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
In what quadrant will an image be if the figure is in quadrant II and is rotated 180° clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
In what quadrant will an image be if the figure is in quadrant III and is rotated 90° clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
In what quadrant will an image be if the figure is in quadrant III and is rotated 90° clockwise?
* In Mathematics, rotation means the Circular movement of an object around one fixed point.
* In rotation, the image after transformation remains constant.
* Hence, it is called as a rigid transformation.
* No Change in shape and size.
* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.
*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
Given Data:
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
>>>Since it is counter clockwise the angle of rotation becomes = 180 degrees.
>>Point (x, y) = (-4, -6)
>>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (-4cos180 + 6sin180 , -6cos180 -6sin180)
= (4 , 6).
***Therefore, the rotation of the point (-4, -6 ) through 180 degrees counter clockwise becomes (4, 6).
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
Given Data:
If the point (-4, -6) rotates 180° counter-clockwise, then the point will be
>>>Since it is counter clockwise the angle of rotation becomes = 180 degrees.
>>Point (x, y) = (-4, -6)
>>>New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (-4cos180 + 6sin180 , -6cos180 -6sin180)
= (4 , 6).
***Therefore, the rotation of the point (-4, -6 ) through 180 degrees counter clockwise becomes (4, 6).
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
Given Data:
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
>>>Since, it is counter clockwise rotation angle of rotation becomes = 90 degrees.
>>point (x, y)= (4, 6)
*New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (4cos90 - 6sin90 , 6cos90 + 4sin90)
= (-6 , 4).
***The rotation of the point (4, 6 ) through 90 degrees counter clockwise becomes (-6, 4).
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
Given Data:
If the point (4, 6) rotates 90° counter-clockwise, then the point will be
>>>Since, it is counter clockwise rotation angle of rotation becomes = 90 degrees.
>>point (x, y)= (4, 6)
*New Coordinates are:
= (x cos - y sin , y cos + x sin).
= (4cos90 - 6sin90 , 6cos90 + 4sin90)
= (-6 , 4).
***The rotation of the point (4, 6 ) through 90 degrees counter clockwise becomes (-6, 4).
If the point (2, 3) rotates 90°clockwise, then the point will be
Given data:
If the point (2, 3) rotates 90°clockwise, then the point will be
>>>Since, it is clockwise rotation angle of rotation becomes negative that is = -90.
>>And the point (x, y) = (2, 3).
>>>Hence, the new coordinates are:
= (x cos - y sin , y cos + x sin).
= (2 cos(-90) - 3 sin(-90) , 3 cos(-90) + 2 sin(-90))
= (3 ,-2).
**Hence, the rotation of the point (2, 3) through 90 degrees clockwise is (3, -2).
If the point (2, 3) rotates 90°clockwise, then the point will be
Given data:
If the point (2, 3) rotates 90°clockwise, then the point will be
>>>Since, it is clockwise rotation angle of rotation becomes negative that is = -90.
>>And the point (x, y) = (2, 3).
>>>Hence, the new coordinates are:
= (x cos - y sin , y cos + x sin).
= (2 cos(-90) - 3 sin(-90) , 3 cos(-90) + 2 sin(-90))
= (3 ,-2).
**Hence, the rotation of the point (2, 3) through 90 degrees clockwise is (3, -2).
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
>>First step is to rotate the point (x, y) through 180 degrees clockwise.
* Hence, the angle of rotation becomes = -180
The new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x, -y).
***Therefore, the rotation of a point (x, y) through 180 degrees clockwise gives (-x, -y).
>>>similarly, the rotation of the point (x, y) through 180 degrees counter clockwise gives:
*The new Coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Therefore, the rotation of the point (x, y) through 180 degrees counter clockwise gives (-x, -y)
>>>Hence, we can say that the rotation of the point (x, y) through any direction yields (-x, -y).
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 180° both clockwise and anti-clockwise will be
>>First step is to rotate the point (x, y) through 180 degrees clockwise.
* Hence, the angle of rotation becomes = -180
The new coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(-180) - y sin(-180) , y cos(-180) + x sin(-180))
= (-x, -y).
***Therefore, the rotation of a point (x, y) through 180 degrees clockwise gives (-x, -y).
>>>similarly, the rotation of the point (x, y) through 180 degrees counter clockwise gives:
*The new Coordinates are:
= (x cos - y sin , y cos + x sin)
= (x cos(180) -y sin(180) , y cos(180) + x sin(180))
= (-x , -y).
***Therefore, the rotation of the point (x, y) through 180 degrees counter clockwise gives (-x, -y)
>>>Hence, we can say that the rotation of the point (x, y) through any direction yields (-x, -y).
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
>>>The first step is to rotate a point (x, y) through 270 degrees clockwise
* Angle of rotation becomes -270
* Then, the coordinates after rotation :
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y cos(-270) + x sin(-270))
= (-y, x).
>>>Second step is to rotate (-y, x) through 90 degrees counter clockwise
* Angle of rotation becomes 90 degrees.
* Then , the new coordinates after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (-y cos(90) - x sin(90) , x cos(90) -y sin(90))
= (-x , -y).
***Therefore the rotation of a point (x, y) through 270 degrees clockwise and 90 degrees counter clockwise becomes (-x, -y).
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
Given Data:
In rotation, the point (x, y) after moving 270° clockwise and 90° counter-clockwise will be
>>>The first step is to rotate a point (x, y) through 270 degrees clockwise
* Angle of rotation becomes -270
* Then, the coordinates after rotation :
= (x cos - y sin , y cos + x sin)
= (x cos(-270) - y sin(-270) , y cos(-270) + x sin(-270))
= (-y, x).
>>>Second step is to rotate (-y, x) through 90 degrees counter clockwise
* Angle of rotation becomes 90 degrees.
* Then , the new coordinates after rotation becomes:
= (x cos - y sin , y cos + x sin)
= (-y cos(90) - x sin(90) , x cos(90) -y sin(90))
= (-x , -y).
***Therefore the rotation of a point (x, y) through 270 degrees clockwise and 90 degrees counter clockwise becomes (-x, -y).
