Chapter 4 4 9 Isosceles and Equilateral Triangles
- Slides: 22
Chapter 4 4 -9 Isosceles and Equilateral Triangles
Objectives Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles.
Isosceles triangles O 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#1 O The length of YX is 20 feet. O O Explain why the length of YZ is the same. The m YZX = 180 – 140, so m YZX = 40°. O Since YZX X, ∆XYZ is isosceles by the Converse of the Isosceles Triangle Theorem. O Thus YZ = YX = 20 ft.
Example 2: Finding the Measure of an Angle O Find m F.
Example#3 O Find m G
Example#4 O Find m N
Student guided practice O Do problems 3 -6 in your book pg. 288
Equilateral triangles O The following corollary and its converse show the connection between equilateral triangles and equiangular triangles.
Equilateral Triangle
Example#5 O Find the value of x.
Example#6 O Find the value of y.
Example#7 O 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.
Solution O Proof: O Draw a diagram and place the coordinates as shown.
Solution O By the Midpoint Formula, the coordinates of X are (a, b), and Y are (3 a, b). O By the Distance Formula, XY = √ 4 a 2 = 2 a, and AC = 4 a. O Therefore XY = 1/2 AC.
Example #9 O What if. . . ? The coordinates of isosceles ∆ABC are A(0, 2 b), B(-2 a, 0), andy C(2 a, 0). X is the midpoint of AB, and Y is the A(0, 2 b) midpoint of AC. Prove ∆XYZ is isosceles. X Y x Z B(– 2 a, 0) C(2 a, 0)
Solution O 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 = √a 2+b 2. O So XZ YZ and ∆XYZ is isosceles.
Homework O Do problems 13 -20 in your book page 289
Closure O Today we learned about isosceles and equilateral triangles O Next class we are going to learned about Perpendicular and angle bisector
- Isosceles and equilateral
- Trigonometry maze answer key
- Congruency in isosceles and equilateral triangles
- Lesson 4-8 isosceles and equilateral triangles
- How to find x in an equilateral triangle
- Corollary to the converse of base angles theorem
- 4-6 isosceles and equilateral triangles
- 4-5 isosceles and equilateral triangles
- Isosceles and equilateral triangles notes
- Notes 4-9 isosceles and equilateral triangles
- 4-8 isosceles and equilateral triangles
- Equilateral triangle corollary
- Right angled isosceles triangle
- Triangles based on sides
- Vertex angle of an isosceles triangle definition
- 3 sided polygon
- Midsegments of triangles unit 7 lesson 1
- A student used a compass and a straightedge to construct ce
- Trapezoid
- Apothem of a square
- Heptagon angle
- How many planes of symmetry does a square based prism have
- Height of an equilateral triangle