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Geometry Day 2 Notes Name_________________________ WARM UP Classify the triangle given the information. 1. Angle measures: 60°, 60°, 60° 3. In PQR, P R and the measure of measure of each angle. Find the value of x. 4. 2. Side lengths: 5 ft, 7 ft, 9 ft Q is twice the measure of R. 5. Find the 80 x 2x 4x (3x - 22) Today, we will understand isosceles and equilateral triangles And You will be able to find angle measures and side lengths in these triangles Using Isosceles and Equilateral Triangles Isosceles Triangle Legs – Vertex angle – Base – Base angles – 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. Examples Find the value of x. 1. 2. 16 5x + 5 60 60 17 x 35 Find the value of x and y. 3. x 9y 4. 5. 6. 3y (x - 2) (4x + 10) Find the perimeter of the triangle. 7. 8. (4x + 3) m (7x - 13) in. (x + 29) in. (3x + 5) in. In the following, fill in the blank will ALWAYS, SOMETIMES, NEVER 9. Obtuse triangles are ____________ isosceles. 10. If a triangle is equilateral then it is ____________ equiangular. 11. A right triangle __________ is an equilateral triangle. 12. Isosceles triangles are __________ equilateral. (8x - 15) m (5x + 8) m