Choose whether the given statement is true or false.

In the given figure, if △ABE≅△ACD , Is that △ADE∼△ABC.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

△ABE ≅ △ACD (Given)
When two triangles are given to be congruent to each other, the corresponding sides and angles of both triangles are congruent to each other using CPCT.
⇒AB=AC, BE=CD, AE=AD are corresponding equal sides of two triangles.
⇒∠ABE=∠ACD, ∠BAE=∠CAD, ∠AEB=∠ADC are corresponding equal angles of two triangles.
Since, AB=AC, AE=AD
Then we can write the fraction

\frac{AD}{AB} = \frac{AE}{AC}

...............… (1)
We will prove the two triangles △ADE, △ABC similar to each other.
In △ADE, △ABC;

\frac{AD}{AB} = \frac{AE}{AC}

{From (1)}
∠BAE = ∠CAD{Common angle}
We have two sides in one triangle that are proportional to two sides in another triangle, and both triangles have angles that are equal.
Then by SAS similarity theorem,
∴△ADE∼△ABC
Therefore the answer is TRUE.

Watch 3-min video & get full concept clarity