Test: Criteria for Similar Triangles - Grade 10 MCQ

Since DE=AB means that there ratio is 1 which means corresponding sides are equal.Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.So they are congruent.

The triangles are similar by SAS criterion, So we have, Angle A+Angle B + Angle C=180
x=180-30-80=70 degrees 

We have Angle ADE= Angle ABC
And ANGLE A is common, So by AA criterion of similarity the two triangles are similar so AD/AB=DE/BC
x=5*4/3=6.7

We have 
=2/4=½
So, =½
AC=8/2=4cm

Thus, the measure of ∠E:  95°

Area of triangle = 1/2 *base*height
Area of ABD=1/2 *BD*2
Area of  BDC=1/2*BD*3

We have Angle C common and Angle B = Angle D
So in similarity we write the name of the triangle in such an order in which the corresponding alphabets denote equal angles . this means that ΔABC ~ ΔBDC that says Angle A = Angle B, Angle B = Angle D, and Angle C = Angle C

Ratios of perimeter of similar triangles are equal to the ratio of their sides.
So Perimeter of ABC/perimeter of DEF=15/25=⅗
AB/DE=⅗
DE=6*5/3=10

Solution : 

The correct option is Option C.

∆ ABC ~ ∆ BDC = AD/AB = BD/BC = ⅔ = BD/4 = BD = 8/3