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Right Triangles

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.

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Right Triangles

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  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 • 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

  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 SAS ASA SSS HL AAS Triangle Congruence isosceles equilateral properties

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