Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Mathematics

Grade9

Easy

Question

Which of the statements is true in the case of the given triangle?

$\frac{A B}{B C} = \frac{A D}{D C}$
$\frac{B D}{A B} = \frac{D C}{B C}$
$\frac{D C}{B C} = \frac{A D}{A B}$
$\frac{A B}{B D} = \frac{B C}{D C}$

hint Hint:

the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

The correct answer is: $fraction numerator A B over denominator B C end fraction equals fraction numerator A D over denominator D C end fraction$

By angle bisector theorem, we have
DC/BC = AD/AB.
Hence, the correct option is A.

The base is divided in the same ratio as the sides containing the angle.

Related Questions to study

To find the value of p, which statements can be used?

Her, the value of p is 43.5.

To find the value of p, which statements can be used?

MathematicsGrade9

Her, the value of p is 43.5.

In the figure, to find the value of x which theorem can be used?

Here, the value of x is 10.

In the figure, to find the value of x which theorem can be used?

MathematicsGrade9

Here, the value of x is 10.

$text In the given triangle end text fraction numerator L K over denominator K J end fraction equals fraction numerator L M over denominator M N end fraction text then end text$

It is also called basic proportionality theorem.

$text In the given triangle end text fraction numerator L K over denominator K J end fraction equals fraction numerator L M over denominator M N end fraction text then end text$

MathematicsGrade9

It is also called basic proportionality theorem.

parallel

Find the length of the segment AB

It is also called basic proportionality theorem or Thales' theorem.

Find the length of the segment AB

MathematicsGrade9

It is also called basic proportionality theorem or Thales' theorem.

In the given triangle $fraction numerator B D over denominator D A end fraction equals fraction numerator B E over denominator E C end fraction$ then the line segment DE ll AC

It is also called midpoint theorem.

In the given triangle $fraction numerator B D over denominator D A end fraction equals fraction numerator B E over denominator E C end fraction$ then the line segment DE ll AC

MathematicsGrade9

It is also called midpoint theorem.

If the line divides the two sides of the triangle proportionally then the line is

If the line divides the two sides of the triangle proportionally then the line is

MathematicsGrade9

parallel

If two triangles are similar then their corresponding sides are

If two triangles are similar then their corresponding sides are

MathematicsGrade9

If a ray bisects an angle of a triangle, then it divides the opposite side into segments

If a ray bisects an angle of a triangle, then it divides the opposite side into segments

MathematicsGrade9

If three parallel lines intersect two transversals,

If three parallel lines intersect two transversals,

MathematicsGrade9

parallel

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

MathematicsGrade9

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

MathematicsGrade9

If a line parallel to one side of a triangle intersects the other two sides

If a line parallel to one side of a triangle intersects the other two sides

MathematicsGrade9

parallel

Polygons are similar when

Polygons are similar when

MathematicsGrade9

Identify the similarity criteria if the two triangles in the figure are similar

Identify the similarity criteria if the two triangles in the figure are similar

MathematicsGrade9

If the area of two similar triangles is 144 and 225, respectively, then what is the scale factor of similar triangles?

If the area of two similar triangles is 144 and 225, respectively, then what is the scale factor of similar triangles?

MathematicsGrade9

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.