1. Right Triangles
Brett Solberg AHS ‘11-’12

2. Warm-up
1) What is the measure of any angle in an equilateral triangle?
2) Solve for x.
Do you have any questions from your homework?

3. Homework Review pg 230 #8 Square and rectangle have a common side.
#9 – Five fence meet at a point to form angles x, 2x, 3x, 4x, and 5x. Solve for x.

4. Calendar Today – 4.6/4.7 Thursday – Chapter 4 Review
Monday – Chapter 4 Test
all late work and missing quizzes due

5. Todays Agenda Partner Activity Right Triangles
Using shortcuts
Right Triangles
Prove right triangles congruent
Hypotenuse Leg Theorem
Proving Overlapping Triangles are Congruent

6. Partner Activity Get into pairs Complete the worksheet using
SSS
SAS
ASA
AAS
You have 5 minutes

7. Right Triangle Hypotenuse Acute Angles Leg Leg
Triangle with a 90˚ angle.
Hypotenuse
Side opposite the right angle
The longest side length
Legs
other side lengths
Right Angle
Acute Angles
Acute Angles
Hypotenuse
Leg
Leg

8. Deep Thoughts Why is the hypotenuse always the longest side length?
Are the other angles always acute?

9. Comic

10. Hypotenuse-Leg Theorem
If the hypotenuse and leg of two right triangles are congruent, then the triangles are congruent.

11. Example 2 Triangle XYZ is isosceles X is the vertex
XM is perpendicular bisector of ZY
Tri XMY ≅ Tri XMZ?

12. Overlapping Triangles
Separate and re-draw the triangles
Identify Corresponding Angles
D ~ E
F ~ H
G ~ G
Identify Corresponding Side Lengths
DG ~ EG
GF ~ GH
DF ~ EH

13. Overlapping Triangles
Common sides or angles
Congruent Shared sides or angles

14. Overlapping Triangles
Separate and find common angle or side

15. Overlapping Triangles

16. #6 - 2 column proof Statement Reason AX ≅ AY Given
∠AYB ≅ ∠CXA All right angles are congruent
∠A ≅ ∠A Reflexive Property
Tri BYA ≅ Tri CXA ASA Postulate

17. Toolbox HL ASA SAS AAS Triangle Congruence SSS isosceles
equilateral properties