Isosceles, Equilateral, and Right TrianglesChapter 4.6

Isosceles Triangle TheoremIsosceles The 2 Base s are Base angles are the angles opposite the equal sides.

Isosceles Triangle Theorem

Isosceles Triangle Theorem

Sample ProblemSolve for the variablesmA = 32mB = (4y) mC = (6x +2)

6x + 2 = 326x = 30 x = 532 + 32 + 4y = 1804y + 64 = 1804y = 116 y = 29

Lesson 6 Ex2Find the Measure of a Missing Angle120o180o 120o = 60o30o30o30o180o 30o = 150o75o75o

Lesson 6 CYP2ABCDA.25B.35C.50D.130

Lesson 6 CYP3ABCDA. Which statement correctly names two congruent angles?

Lesson 6 CYP3ABCDB. Which statement correctly names two congruent segments?

Equilateral Triangle TheoremEquilateral EquiangularEach angle = 60o !!!

Lesson 6 Ex4Answer: 105Use Properties of Equilateral TrianglesSubtractionLinear pair Thm.Substitution

Lesson 6 CYP4ABCDA.x = 15B.x = 30C.x = 60D.x = 90

Lesson 6 CYP4ABCDA.30B.60C.90D.120

Dont be an ASS!!!Angle Side Side does not work!!!(Neither does ASS backward!)It can not distinguish between the two different triangles shown below.However, if the angle is a right angle, then they are no longer called sides. They are called

Hypotenuse-Leg TheoremIf the hypotenuse and one leg of a right triangle are congruent to the corresponding parts in another right triangle, then the triangles are congruent.

ABC XYZ Why?HL Theorem

Prove XMZ YMZStepReasonGivenGivenmZMX = mZMY = 90oDef of linesReflexiveHL ThmZMX ZMY

Corresponding Parts of Congruent Triangles are CongruentGiven ABC XYZYou can state that:A XB YC Z

Suppose you know that ABD CDB by SAS Thm. Which additional pairs of sides and angles can be found congruent using Corr. Parts of s are ?

Lesson 6 CYP1Complete the following two-column proof.Proof: 4.ReasonsStatements1. Given2. Isosceles Theorem 1.

2.3.3. Given4. Def. of midpoint

Lesson 6 CYP1ABCDProof: Complete the following two-column proof.SAS Thm.Corr. Parts of s are

HomeworkCh 4-6 pg 248 1 10, 14 27, 32, 33, 37 39, & 48Reminder!Midpoint Formula:Video C