Using Isosceles and Equilateral Triangles
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1 Geometry Unit 4: Intro to Triangles Name Day 2: Isosceles, Equilateral, and Sum of Triangles Notes Block Date Today, we will understand isosceles and equilateral triangles And you will be able to find angle measures and side lengths in these triangles Isosceles Triangle Using Isosceles and Equilateral Triangles Legs The sides of an isosceles triangle Vertex angle The angles formed by the of an isosceles triangle Base The side that is not a. Base angles The angles formed by the and the. Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. Equilateral Triangle Corollary to the Base Angles Theorem If a triangle is equilateral, then it is equiangular. Corollary to the Converse of Base Angles Theorem If a triangle is equiangular, then it is equilateral.
2 Examples 1. Find the value of x. 2. Find the measurement of angle A A 60 x 3. Find the value of x. 4. Find the value of x. 5. Find the value of x and y. 6. Find the value of x and y. (11y-15)
3
4 Geometry Unit 4 Day 2 Isosceles, Equilateral, and Sum of Triangles Practice Name Block Date Find the unknown measure. 1. H 2. L 3. P 6?? 18 G J K 70? M N Q Find the value of x. 4. S 5. (7x + 5) (x + 47) 6. A 10 5x 10 G J B R 10 T H C 9 x F 8. x 2 E 40 (11x - 18) D x x x
5 Find the values of x and y (3x + 8) (5x + 6) (y - 9) (8y + 10) (6y - 5) (10y - 41) 53 (12x + 22) Find the perimeter of the triangle (5x - 7) in. (x + 6) in. (3x + 2) in. 14 in. (7x - 17) m (4x - 5) m 12 in. (10x - 32) in. (2x + 3) m
6 Name: Date: Missing Angles in Triangles The sum of the angles of any triangle is Find all the missing angles in the triangles. Write each answer in the line provided beside the corresponding letter. 72 H G 32.1 J G I O. Perez, C B A E 30.4 F K O D P 35.7 N L 75 M A B C D E F G H I J K L M N O P
7 Name: Date: Missing Angles in Triangles Find all the missing Angles in the triangles. Write each answer in the line provided beside the corresponding letter. Notice that angle C is in an equilateral triangle and angle D is in an isosceles triangle. E I K The sum of the angles of any triangle is U 55 L H D M 69 F G J A Q P R S C 48 O. Perez, 2016 N B O T A B C D E F G H I J K L M N O P Q R S T U
8 Geometry Unit 4 Day 2 Isosceles, Equilateral, and Sum of Triangles Additional Practice Find the values of x and y (3x - 11) (2x + 11) Name Block Date (15x - 13) 2y 2y (8x + 29) Find the perimeter of the triangle. Find the values of x, y, and z x 12 ft (9x - 11) ft y (5x + 16) ft z 64 x 5. Find the value of x, then find the measure of each angle. (2x - 45) (3x + 10) 6. Given: 4 = 6x = 2x + 55 Find the following angle measures. m 1= m 2 = m 3 = m 4 =
9 7. If one angle of a linear pair is a right angle then the other angle must be A straight B acute C obtuse D right 8. If one angle of a linear pair is obtuse then the other angle must be A straight B acute C obtuse D right 9. Two adjacent angles add up to 180 degrees. We would call these A a linear pair B supplementary angles C complementary angles D a right angle 10. Two angles add up to 90 degrees. We would call these A a linear pair B supplementary angles C complementary angles D a right angle Fill in the blank. 11. In any right triangle, there can only be right angle(s). 12. Equiangular triangles have sides that have the same length. 13. The base angles in an isosceles triangle are. 14. The congruent sides of an isosceles triangle are called the. In the following, fill in the blank will ALWAYS, SOMETIMES, NEVER 15. Obtuse triangles are isosceles. 16. If a triangle is equilateral then it is equiangular. 17. A right triangle is an equilateral triangle. 18. Isosceles triangles are equilateral.
10 Challenge Questions! Types of some of these questions will be on the test. Review all and ask questions! 1. Find x and y. x 9y 2. Find x and y. 3. Find x and y. 3y (x - 2) (4x + 10) 4. Find the perimeter of the triangle. (7x - 13) in. (x + 29) in. (3x + 5) in.
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