Question

It is given that ∆ABC ~ ∆PQR. Is it true to say that Angle B=Angle P and Angle A=Angle R? Why?

Answer 1

Given,

Triangle PQR

PQ = PR

Angle P = 36 degrees

An isoceles Triangle,

  Since two sides of a triangle are equal doesn't implicitly imply that it is an isoceles triangle, it can also be an equilateral triangle. The second fact confirms this for us that one angle is 36 degrees and so it cannot be an equilateral triangle.

Now we know that,

Sum of angles is 180 degrees, &

Angles opposite to equal sides are equal

Side opposite to greater angle is greater than side opposite to smaller angle.

So that in this triangle two angles are same (Say x), and third angle is 36 degrees.

So,

x+x+36 = 180,or

x=72

Answer 2

Given : ΔABC ~ ΔPQR

To Find : is it true to say angle B = angle P and angle A = angle R

if not why

Solution:

ΔABC ~ ΔPQR

corresponding parts of similar triangle are equal

Hence

∠A = ∠P

∠B = ∠Q

∠C = ∠R

∠A = ∠P     hence ∠A ≠ ∠R

∠B = ∠Q     hence ∠B ≠ ∠P

so it  is not true to say angle B = angle P and angle A = angle R

As corresponding parts should be equal

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