+ All Categories
Home > Documents > Chapter 4 4-9 Isosceles and Equilateral Triangles.

Chapter 4 4-9 Isosceles and Equilateral Triangles.

Date post: 29-Dec-2015
Category:
Upload: isabel-webb
View: 245 times
Download: 1 times
Share this document with a friend
Popular Tags:
22
Chapter 4 4-9 Isosceles and Equilateral Triangles
Transcript

Chapter 4 4-9 Isosceles and Equilateral

Triangles

Objectives

Prove theorems about isosceles and equilateral triangles.

Apply properties of isosceles and equilateral triangles.

Isosceles trianglesO Recall that an isosceles triangle has at

least two congruent sides. The congruent sides are called the legs. The vertex angle is the angle formed by the legs. The side opposite the vertex angle is called the base, and the base angles are the two angles that have the base as a side.

O 3 is the vertex angle.

O 1 and 2 are the base angles

Theorems for isosceles triangles

Example#1O The length of YX is 20 feet.

O Explain why the length of YZ is the same.O

O Since YZX X, ∆XYZ is isosceles by the Converse of the Isosceles Triangle Theorem.

O Thus YZ = YX = 20 ft.

The mYZX = 180 – 140, so

mYZX = 40°.

Example 2: Finding the Measure of an Angle

O Find mF.

Example#3O Find mG

Example#4O Find mN

Student guided practice

O Do problems 3-6 in your book pg.288

Equilateral trianglesO The following corollary and its

converse show the connection between equilateral triangles and equiangular triangles.

Equilateral Triangle

Example#5O Find the value of x.

Example#6O Find the value of y.

Example#7O Find the value of JL

Student guided practice

O Do problems 7-10 in your book 288

Example#8 Using coordinate proofs

O Prove that the segment joining the midpoints of two sides of an isosceles triangle is half the base.

O Given: In isosceles ∆ABC, X is the mdpt. of AB, and Y is the mdpt. of AC.

O Prove: XY = 1/2 AC.

SolutionO Proof:O Draw a diagram and place the

coordinates as shown.

SolutionO By the Midpoint Formula, the

coordinates of X are (a, b), and Y are (3a, b).

O By the Distance Formula, XY = √4a2 = 2a, and AC = 4a.

O Therefore XY = 1/2 AC.

Example #9 O What if...? The coordinates of

isosceles ∆ABC are A(0, 2b), B(-2a, 0), and C(2a, 0). X is the midpoint of AB, and Y is the midpoint of AC. Prove ∆XYZ is isosceles.

x

A(0, 2b)

B(–2a, 0) C(2a, 0)

y

X Y

Z

SolutionO By the Midpoint Formula, the

coordinates. of X are (–a, b), the coordinates. of Y are (a, b), and the coordinates of Z are (0, 0) . By the Distance Formula, XZ = YZ = √a2+b2 .

O So XZ YZ and ∆XYZ is isosceles.

HomeworkO Do problems 13-20 in your book

page 289

Closure O Today we learned about isosceles

and equilateral trianglesO Next class we are going to learned

about Perpendicular and angle bisector


Recommended