Maths-
General
Easy
Question
Triangle DEF (not shown) is similar to triangle ABC above, where side DE corresponds to side AB, side DF corresponds to side AC , and DE = AB. What is the measure of angle DEF ?
The correct answer is:
HINT : In similar triangles the corresponding angles will be equal in the same order of the similarity.
Explanation: Given ΔDEF is similar to ΔABC
Step 1: Check the similarity order
Side DE corresponds to AB (ΔDEF ~ ΔABC)
Side DF corresponds to AC (ΔDEF ~ ΔABC)
Verified successfully that ΔDEF ~ ΔABC are in correct order of similarity then
Step 2:Finding all angles of ΔABC
In ΔABC ,∠A = 90° ,∠B = 37°(given in diagram)
But ∠A +∠B +∠C = 180°( sum of angles in a triangle )
90° + 37°+∠C =180°
∠C =180°- 90° - 37°
∴∠C =53°=∠ACB
Step 3:
∠DFE = ∠ACB (By similarity of triangles)
∠DFE=∠ACB= 53°
∴∠DFE = 53°
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