Isosceles, Equilateral, and Right Triangles

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Presentation transcript:

Isosceles, Equilateral, and Right Triangles Chapter 4.6

Isosceles Triangle Theorem Isosceles   The 2 Base s are  Base angles are the angles opposite the equal sides. 

Isosceles Triangle Theorem B If AB  BC, then A  C

Isosceles Triangle Theorem B If A  C then AB  BC

Sample Problem Solve for the variables mA = 32° mB = (4y)° mC = (6x +2)° A C B 32 + 32 + 4y = 180 4y + 64 = 180 4y = 116 y = 29 6x + 2 = 32 6x = 30 x = 5

Find the Measure of a Missing Angle 180o – 120o = 60o 180o – 30o = 150o Lesson 6 Ex2

A. 25 B. 35 C. 50 D. 130 A B C D Lesson 6 CYP2

A. Which statement correctly names two congruent angles? B. C. D. A B C D Lesson 6 CYP3

B. Which statement correctly names two congruent segments? D. A B C D Lesson 6 CYP3

Equilateral Triangle Theorem Equilateral   Equiangular  Each angle = 60o !!!

Use Properties of Equilateral Triangles Linear pair Thm. Substitution Subtraction Answer: 105 Lesson 6 Ex4

A. x = 15 B. x = 30 C. x = 60 D. x = 90 A B C D Lesson 6 CYP4

A. 30 B. 60 C. 90 D. 120 A B C D Lesson 6 CYP4

Don’t 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   Theorem If 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  YMZ Given Given Reflexive ZMX  ZMY HL   Thm Step Reason X Y Z M Given Given mZMX = mZMY = 90o Def of  lines Reflexive ZMX  ZMY HL   Thm

Corresponding Parts of Congruent Triangles are Congruent Given ΔABC  ΔXYZ You can state that: A  X B  Y C  Z AB  XY BC  YZ CA  ZX

Suppose you know that ABD  CDB by SAS   Thm 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 ?

Complete the following two-column proof. Statements Reasons 1. 1. Given 2. 2. Isosceles Δ Theorem 3. 3. Given 4. 4. Def. of midpoint Lesson 6 CYP1

SAS   Thm. Corr. Parts of  s are  Complete the following two-column proof. Proof: 4. Reasons Statements 4. Def. of midpoint 5. ______ 6. 6. ? 5. ΔABC ΔADC ? A B C D SAS   Thm. Corr. Parts of  s are  Lesson 6 CYP1

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