Given triangle PRS is congruent to triangle CFH, find the values of x, y, and z.

The values of x, y, and z are;

x = 23

x = 23y = 7

x = 23y = 7z = 11

We are told that triangle PRS is congruent to triangle CFH.

Since both triangles are congruent, by inspection we can see that;

m<R = m<F

m<F is a right angle = 90°. Thus;

13y - 1 = 90

13y = 90 + 1

13y = 91

y = 91/13

y = 7

Also by inspection;

PS = CH

2x - 7 = 39

2x = 39 + 7

2x = 46

x = 46/2

x = 23

Since m<R is 90°, then;

m<S = 180 - (90 + 28)

m<S = 62°

By inspection;

m<S = m<H

Thus;

6z - 4 = 62

6z = 66

z = 66/6

z = 11

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x = 23

y = 7

z = 11

Step-by-step explanation:

Since ∆PRS ≅ ∆CFH, therefore,

m<R = m<F

13y - 1 = 90° (substitution)

Add 1 to both sides

13y - 1 + 1 = 90 + 1

13y = 91

Divide both sides by 13

13y/13 = 91/13

y = 7

Since ∆PRS ≅ ∆CFH, therefore,

PS = CH

2x - 7 = 39 (substitution)

Add 7 to both sides

2x - 7 + 7 = 39 + 7

2x = 46

Divide both sides by 2

2x/2 = 46/2

x = 23

Since ∆PRS ≅ ∆CFH, therefore,

m<S = m<H

Find m<S

m<S = 180 - (m<P + m<R) (sum of ∆)

m<S = 180 - (28 + (13y - 1)) (substitution)

Plug in the value of y

m<S = 180 - (28 + (13)(7) - 1))

m<S = 180 - (28 + 91 - 1)

m<S = 180 - 118

m<S = 62°

Therefore, since m<S = m<H,

62° = 6z - 4 (substitution)

Add 4 to both sides

62 + 4 = 6z - 4 + 4

66 = 6z

Divide both sides by 6

66/6 = 6z/6

11 = z