MATH 8 REVIEW SESSION

LESSON 6

Hypotenuse -Leg (HyL) Congruence

Theorem

&

Hypotenuse- Acute Angle (HyA)

Congruence Theorem

If Hypotenuse AC ≅ XZ

Leg AB ≅ XY

then Rt△ ABC ≅ Rt△ XYZ

EXAMPLE #1

Multiple Choice

If Hypotenuse AC ≅ ____

Leg AB ≅ ____

then Rt△ ___ ≅ Rt△ ___

• Hypotenuse AC ≅ ED

• Hypotenuse AC ≅ DF

• Hypotenuse AC ≅ EF

• Hypotenuse AC ≅ AC

Multiple Choice

If Hypotenuse AC ≅ ____

Leg AB ≅ ____

then Rt△ ___ ≅ Rt△ ___

• Leg AB ≅ ED

• Leg AB ≅ DF

• Leg AB ≅ EF

• Leg AB ≅ AB

Multiple Choice

If Hypotenuse AC ≅ ____

Leg AB ≅ ____

then Rt△ ___ ≅ Rt△ ___

• Rt△ ABC ≅ Rt△ FDE

• Rt△ ABC ≅ Rt△ EDF

• Rt△ ABC ≅ Rt△ EFD

• Rt△ ABC ≅ Rt△ EFB

EXAMPLE #2

If Hypotenuse AC ≅ XZ

Angle C ≅ Z

then Rt△ ABC ≅ Rt△ XYZ

Multiple Choice

If Hypotenuse PR ≅ _____

Angle U ≅ ____

then Rt△ ____ ≅ Rt△ ____

• Hypotenuse PR ≅ RQ

• Hypotenuse PR ≅ TU

• Hypotenuse PR ≅ SU

• Hypotenuse PR ≅ PR

Multiple Choice

If Hypotenuse PR ≅ _____

Angle U ≅ ____

then Rt△ ____ ≅ Rt△ ____

• Angle U ≅ P

• Angle U ≅ S

• Angle U ≅ Q

• Angle U ≅ R

Multiple Choice

If Hypotenuse PR ≅ _____

Angle U ≅ ____

then Rt△ ____ ≅ Rt△ ____

• Rt△ PQR ≅ Rt△ SUT

• Rt△ PQR ≅ Rt△ UST

• Rt△ PQR ≅ Rt△ STU

• Rt△ PQR ≅ Rt△ STR

PROBLEM SOLVING - #1

​Solution:

Hypotenuse CD ≅ JH

y + 50 = 6y

50 = 6y - y

50 = 5y

50 = 5y

5 5

y = 10

PROBLEM SOLVING - #1

​Solution:

Leg CB ≅ JI

3z = z + 18

3z - z = 18

2z = 18

2z = 18

2 2

z = 9

PROBLEM SOLVING #2

​Solution:

Hypotenuse KJ ≅ FH

49 = b + 43

49 - 43 = b

6 = b

PROBLEM SOLVING #2

​Solution:

Leg KI ≅ FG

c + 34 = 44

c = 44 - 34

c = 10

Fill in the Blank

1. What is the value of W?

W = ____

Fill in the Blank

1. What is the value of V?

V = ____

Fill in the Blank

2. What is the value of W?

W = ____

Fill in the Blank

2. What is the value of V?

V = ____