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Section 4.6 Isosceles, Equilateral and Right Triangles

Section 4.6 Isosceles, Equilateral and Right Triangles. Review: Ways to Prove Triangles are Congruent. SSS Congruence Postulate SAS Congruence Postulate ASA Congruence Postulate AAS Congruence Theorem. NEW: Way to Prove Triangles are Congruent. H -L Congruence Theorem

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Section 4.6 Isosceles, Equilateral and Right Triangles

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  1. Section 4.6Isosceles, Equilateral and Right Triangles

  2. Review: Ways to Prove Triangles are Congruent • SSS Congruence Postulate • SAS Congruence Postulate • ASA Congruence Postulate • AAS Congruence Theorem

  3. NEW: Way to Prove Triangles are Congruent • H-L Congruence Theorem Only applies to Right Triangles!States that if the hypotenuses are congruent and one set of legs are congruent then the triangles are congruent!

  4. Isosceles triangle theorems • Base Angles Theorem • If two sides of a triangle are congruent, then the angles opposite them are also congruent. • Converse of the Base Angles theorem • If two angles of a triangle are congruent, then the sides opposite them are also congruent Look at angles and sides that are across from one another!!! If <P and <Q are congruent then sides PR and QR must also be congruent. Likewise, if Sides PR and QR are congruent, then <P and <Q must also be congruent!

  5. 35° x Example 1 – Find the measure of x

  6. b a 15° Example 2 – Find “a” and “b”

  7. m n 10 cm 63° p Example 3 – Find each missing measure

  8. Equilateral Triangles • If a triangle is equilateral, then it is equiangular (each angle measures 60o.) • If a triangle is equiangular (each angle measures 60o), then it is equilateral.

  9. 2x in 12 in Example 4 – Find x

  10. x y Example 5 – find x & y

  11. x° 75° y° x° Example 6 – Find x & y

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