Important Questions: Triangles - Class 10 MCQ

The correct option is Option D.

By using angle sum property, we find third angle

AED = 180° - (70°+50°) = 60°

and DE ll BC 

So, by corresponding angle, we get the value of BCA = 60°.

Since △ABC~△EDF

Then, AB/ED = BC/DF = AC/EF

A) BC/DF = AC/EF

⇒BC.EF=AC.FD   

So, A) is true

B) AB/ED = AC/EF

⇒AB.EF=AC.DE     

So,B) is true

D) AB/ED = BC/DF

BC.DE=AB.EF    

So, D) is not true

Therefore, Option  C is not true

Quadrilaterals are similar if their angles are equal and corresponding sides are proportional.

Since, DE is parallel to BC

→ angle ADE = angle ABC (corresponding angles)

→ angle AED = angle ACB (corresponding angles)

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

ratio of corresponding sides of similar triangles are equal.

AD/AB = DE/BC

AB = AD + DB

AB = 2 + 3 = 5 cm

So,

2/5 = DE/7.5

DE = 2/5 × 7.5

DE = 2 × 1.5

DE = 3 cm.

Then, ΔCAB ~ ΔPQR

Since the two triangles are similar, therefore, they will have their corresponding angles congruent and the corresponding sides in proportion.

Properties of triangles.

to be congruent, the conditions are
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Hypotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, given triangles are not congruent.
But they are similar.