Question

Complete the similarity statement for the two triangles shown. Enter your answer in the box.

Answer 1

ΔDPL ~ ΔQAZ

Because they have 3 congruent angles
∠D = ∠Q
∠P = ∠A
∠L = ∠Z

and corresponded sides have same proportion
DP/QA = PL/AZ = LD/ZQ

Answer 2

In the given figure:

In triangle DPL

DP = 45 ft , DL = 25 ft and LP = 45 ft.

In triangle QAZ

QA = 18 ft, QZ = 10 ft and AZ = 22 ft.

Similar triangles states that the two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

In triangle DPL and triangle QAZ

Corresponding Angles:

`\angle D = \angle Q`

`\angle P = \angle A`

`\angle L = \angle Z`

Now, to find the corresponding sides:

`(DP)/(QA) = (45)/(18) = (5)/(2)`

`(PL)/(AZ) = (55)/(22) = (5)/(2)`

`(DL)/(QZ) = (25)/(10) = (5)/(2)`

Since, the corresponding sides are in proportion i.e,

`(DP)/(QA)=(PL)/(AZ)=(DL)/(QZ)`

then, by Similar triangle definition:

`\triangle DPL \sim \triangle QAZ`