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

Congruent triangles have equal corresponding sides and angle measures

The values of x, y and z are 23, 7 and 11

Because triangle PRS is congruent to triangle CFH, then we have the following congruence statements:

The above highlights mean that:

Add 1 to both sides

Divide both sides by 13

Also, we have:

Add 4 to both sides

Divide both sides by 6

Rewrite as:

Also, we have:

This gives

Add 7 to both sides

Divide both sides by 2

Hence, the values of x, y and z are 23, 7 and 11

Read more about congruent triangles at:

link

x = 23

y = 7

z = 11

Step-by-step explanation:

From ΔPRS,

(13y - 1)° + 28° + m∠S = 180°

m∠S = 180° - (13y + 27)°

m∠S = (153 - 13y)°

Since, ΔPRS ≅ ΔCFH,

m∠R = m∠F

(13y - 1)° = 90°

13y = 91

y = 7

m∠H ≅ m∠S

(6z - 4)° = (153 - 13y)

6z = 153 - 13y + 4

6z = 157 - 13y

6z = 157 - 13(7) [Since, y = 7]

6z = 66

z = 11

PS ≅ CH

(2x - 7) = 39

2x = 46

x = 23