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Discovering Right Triangles and Triangle Congruence

Explore the properties of right triangles and the concept of triangle congruence through engaging activities and deep thought questions. Practice using different postulates and theorems to prove triangles congruent and enhance your understanding of geometric principles.

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Discovering Right Triangles and Triangle Congruence

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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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