Question

Help plz!!! 68 Points!!

Answer 1

Answer:

Refer below explanation.

Step-by-step 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 )

$\frac{QL}{KL}=\frac{16}{40} \\\\\frac{PK}{KM} =\frac{26}{65}$

(reason : ratio of corresponding sides)

Statement 3)

$\frac{QL}{KL}=\frac{16}{40}=\frac{2}{5} \\\\\frac{PK}{KM} =\frac{26}{65}=\frac{2}{5}$

Thus, $\frac{QL}{KL}=\frac{PK}{KM} =\frac{2}{5}$

(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.