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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

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 OampP 50 0 x 2 OampR85 Oy 3 0 6 L class=

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sqdancefan

Answer:

  • x = 2
  • ∠R = 85°
  • y = 3

Step-by-step 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

__

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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