5-2: Right Triangles

1
5-2 Right Triangles

• Expectation
• G2.3.1 Prove that triangles are congruent using
  SSS, SAS, ASA, AAS and that right triangles are
  congruent using the hypotenuse leg condition.
• G2.3.2 Use theorems about congruent triangles to
  prove additional theorems and solve problems.

2
ACT Prep

• If line l is parallel to line m below, what is
  the value of x?
• 12
• 15
• 20
• 24
• 30

l
(x60)
(4x)
m
3
Leg-Leg Condition
What is true about two right triangles that have
congruent legs? Why?
4
Leg-Leg Right Triangle Congruence Theorem (LL)

• In 2 right triangles, if the legs of the first
  are congruent to the legs of the second, then the
  triangles are congruent.

5
Hypotenuse Acute Angle Condition
C
Z
A
B
X
Y
What is true about the right triangles above?
Why?
6
Hypotenuse Acute Angle Right Triangle Congruence
Theorem (HA)

• In 2 right triangles, if the hypotenuse and an
  acute angle of the first are congruent to the
  hypotenuse and an acute angle of the second, then
  the triangles are congruent.

7
Leg Acute Angle Condition
First case
What is true about the triangles above? Why?
8
Leg Acute Angle Condition
Second case
C
Z
A
B
X
Y
What is true about the triangles above? Why?
9
Leg Acute Angle Right Triangle Congruence Theorem
(LA)

• In two right triangles, if a leg and an acute
  angle of the first are congruent to the
  corresponding leg and acute angle of the second,
  then the triangles are congruent.

10
Hypotenuse Leg Condition
What is true about the triangles above? Why?
11
Hypotenuse Leg Right Triangle Congruence
Postulate (HL)

• In 2 right triangles, if the hypotenuse and a leg
  of the first are congruent to the hypotenuse and
  the corresponding leg of the second, then the
  triangles are congruent.

12
Can HL be used to conclude the triangles are
congruent? Justify.
13
Can HL be used to conclude the triangles are
congruent? Justify.
14
What additional information would you need to
prove the triangles are congruent by HL?
B
?ADB ? ?CDB
D
C
A
15
Given XY ? LY, Y is the midpoint of WK and ?W
and ?K are right angles Prove XW ? LK
X
L
Y
K
W
16
Assignment

• pages 249 250,
• 14, 16, 20, 24, 27