Right Triangles Brett Solberg AHS ‘11-’12.

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Presentation transcript:

Right Triangles Brett Solberg AHS ‘11-’12

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?

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.

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

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

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

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

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

Comic

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

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

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

Overlapping Triangles Common sides or angles Congruent Shared sides or angles

Overlapping Triangles Separate and find common angle or side

Overlapping Triangles

#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

Toolbox HL ASA SAS AAS Triangle Congruence SSS isosceles equilateral properties