6.5 Notes: Isosceles and Equilateral Triangles

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Presentation transcript:

6.5 Notes: Isosceles and Equilateral Triangles Lesson Objective: Use properties of isosceles and equilateral triangles. CCSS: G.CO.10, 12 You will need: compass, ruler, colored pens Real-World App: What are the angles of the gable of a house? This is Jeopardy!!!: This is the perimeter of an Isosceles triangular park if its legs are two- thirds of its 6 km base.

Lesson 1: Isosceles Triangles Draw a line 3.5” long and another line 2” as shown. 3.5” 2”

Lesson 1: Isosceles Triangles Skipping down about 4 lines, draw a horizon-tal line about 4” long along a blue line. 3.5” 2”

Lesson 1: Isosceles Triangles Construct Isosceles ∆ABC with base 3.5” and side lengths 2” using a compass. Label the side lengths. A 3.5” C 3.5” 2”

Lesson 1: Isosceles Triangles Measure and label angles A and C. What do you notice? B 2” 2” A 3.5” C 3.5” 2”

Lesson 1: Isosceles Triangles B 2” 2” A 3.5” C Example: If AB BC, then / A / C. 3.5” 2” Isosceles ∆ Theorem: If 2 sides of a ∆ are , then the angles opposite the sides are .

Lesson 1: Isosceles Triangles B 30° 30° A 3.5” C Converse Isosceles Triangle Theorem: Example: if / A / C, then AB CB.

Lesson 2: Congruent Segments and Angles Name two unmarked congruent angles. Name two unmarked congruent segments.

Lesson 3: Equilateral Triangles With only a compass and ruler, construct a 2” equilateral triangle. Start about 6-7 lines down. Work with your partner if you don’t know how to do this. 2”

Lesson 3: Equilateral Triangles B 2” 2” 2” A 2” C Example: If / A / B / C, then AB BC CA. If AB BC CA, then m/ A = m/ B = m/ C = 60°.

Lesson 4: Finding Missing Measures Find each measure. m/ M PN

Lesson 5: Find Missing Values Find the value of each variable. Then find all angle and length measures.

Lesson 6: Real-World App The exterior angle of an Isosceles gable of a house is shown. What are the measures the interior angles of the gable? 145°

Lesson 7: Finding Missing Values Find the value of each variable. Then find the measures of each angle and side length. m/ BAC = m/ B = m/ BCA; AB = 2x + 11, BC = 6x – 9 AE = CE; m/ E = 100°, m/ EAC = 6y – 2, m/ ECA = 4z + 20

6.1(b): Do I Get It? Yes or No 1. Find m/ 1 on the truck below. 2. Find the value of x in the figure above right. Then find the measure of each angle.

6.5: Do I Get It? Yes or No 1. Find each measure. m/ Y YZ Find the value of each variable.