Right TrianglesBrett Solberg AHS ‘11-’12

1) What is the measure of any angle in an equilateral triangle?

2) Solve for x.

Do you have any questions from your homework?

Warm-up

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.

Homework Review

Today – 4.6/4.7 Thursday – Chapter 4 Review Monday – Chapter 4 Test

all late work and missing quizzes due

Calendar

Partner Activity Using shortcuts

Right Triangles Prove right triangles congruent

Hypotenuse Leg Theorem

Proving Overlapping Triangles are Congruent

Todays Agenda

Get into pairs

Complete the worksheet using SSS SAS ASA AAS

You have 5 minutes

Partner Activity

Triangle with a 90˚ angle. Hypotenuse

Side opposite the right angle The longest side length

Legs other side lengths

Right Angle Acute Angles

Right Triangle

Hypotenuse

Leg

LegAcute Angles

Why is the hypotenuse always the longest side length?

Are the other angles always acute?

Deep Thoughts

Comic

If the hypotenuse and leg of two right triangles are congruent, then the triangles are congruent.

Hypotenuse-Leg Theorem

Example 2

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

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

Overlapping Triangles

Common sides or angles Congruent Shared sides or angles

Overlapping Triangles

Separate and find common angle or side

Overlapping Triangles

Overlapping Triangles

#6 - 2 column proof

Statement ReasonAX ≅ AY Given∠AYB ≅ ∠CXA All right angles are congruent∠A ≅ ∠A Reflexive PropertyTri BYA ≅ Tri CXA ASA Postulate

Toolbox

Triangle Congruence

SSS SASASA

AAS

HLisosceles equilateral properties