Question

Help plz!!! 68 Points!!

Complete the following proof.


Given: QK=16, PK=26, MK=65, KL=40

Prove: ∆QPK~∆LMK

Answer 1

Refer below explanation.

Explanation:

Given : two triangles ∆QPK and ∆LMK.

We have to show ∆QPK ≅ ∆LMK.

Two triangles are similar if ratio of the corresponding sides are equal and measure of corresponding angles are equal.

Statement 1)

QK=16, PK=26, MK=65, KL=40 ( Reason: Given)

Statement 2 )

`(QL)/(KL)=(16)/(40) \\\\(PK)/(KM) =(26)/(65)`

(reason : ratio of corresponding sides)

Statement 3)

`(QL)/(KL)=(16)/(40)=(2)/(5) \\\\(PK)/(KM) =(26)/(65)=(2)/(5)`

Thus,
`(QL)/(KL)=(PK)/(KM) =(2)/(5)`

(reason: simplify ratios)

Statement 4)

∠MKL = ∠PQK (reason : Vertically opposite angles)

Statement 5)

∆QPK ≅ ∆LMK (reason : Side-angle-side)

Side angle side similarity criterion states that two angles are similar if the ratio of their corresponding sides and angle between these sides are equal then triangles are similar.