Question

2.2 In isosceles triangle XYZ and triangle RST, XY = XZ and RS = RT, respectively.
(a) If XY = RS and YZ = ST, are the two triangles congruent? Justify
(b) If ZY = 50, what is the measure of ZT?​

Answer 1

Answer:

Construct △RST such that RS=4.5cm,∠RST=40

o

and ST=5.7cm.△RST and △XYZ are similar.

So, their corresponding sides are proportional and corresponding angles are equal.

∴

XY

RS

=

YZ

ST

=

XZ

RT

=

5

3

⇒

XY

4.5

=

YZ

5.7

=

5

3

⇒XY=

3

5

×4.5=7.5cm,YZ=

3

5

×5.7=9.5cm

Also, ∠XYZ=∠RST=40

o

Now, construct △XYZ such that XY=7.5cm,∠XYZ=40

o

and YZ=9.5cm.