Question

In the figure below quadrilateral JKLM is similar to quadrilateral NPQR. Select All the true statements.

J
12
K
20
M
85°
100°
5y + 1
O&P = 50°
0 x = 2.
O&R=85*,
Oy = 3.
0 = 6.
L
R
8
Q
10
7
N
x +4
POSSIBLE
P

Answer 1

• x = 2
• ∠R = 85°
• y = 3

Explanation:

Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.

Relations

Corresponding angles are congruent, so we have ...

∠K≅∠P = 100°

∠M≅∠R = 85°

Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.

JK : NP = 12 : (x+4) ⇒ x+4 = 6 ⇒ x = 2

KL : PQ = ? : 7 ⇒ KL = 14

LM : QR = (5y+1) : 8 ⇒ 5y+1 = 16 ⇒ y = 3

MJ : RN = 20 : 10 . . . . . establishes the ratio for the others

The true statements are ...

• x = 2
• ∠R = 85°
• y = 3

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Additional comment

It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).

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