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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

2. Congruent Polygons

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Exercise 9 Page 243

Corresponding angles have equal measures.

x=7, y=8

Practice makes perfect

Let's analyze the given diagram, where ABCD ≅ EFGH.

To find the values of x and y, we will use the fact that corresponding angles have equal measures. From the given congruence statement, we know that ∠ A ≅ ∠ E and ∠ B ≅ ∠ F. This means that we can equate the measures of these angles to find the values. Let's start with ∠ A and ∠ E.

m∠ A=m∠ E

m∠ A= 28, m∠ E= 4y-4

28= 4y-4

▼

Solve for y

LHS+4=RHS+4

32=4y

.LHS /4.=.RHS /4.

8=y

Rearrange equation

y=8

Similarly, by equating the measures of ∠ B and ∠ F, we can find the value of x.

m∠ B=m∠ F

m∠ B= 135, m∠ F= 10x+65

135= 10x+65

▼

Solve for x

LHS-65=RHS-65

70=10x

.LHS /10.=.RHS /10.

7=x

Rearrange equation

x=7

We found that the values of x and y are 7 and 8 respectively.

Subchapter links

Communicate Your Answer p.239

Monitoring Progress p.241-242