Homework 4.1 – Triangle Sum & Classifying Triangles Name: __________________________ Block: _______ Date: ___________ Complete the sentence with always, sometimes, or never. 1. An isosceles triangle is ____________________ a right triangle. 2. An obtuse triangle is ____________________ a right triangle. 3. A right triangle is ____________________ an equilateral triangle. 4. A right triangle is ____________________ an isosceles triangle. Find the value of x. Then classify the triangle by its angles. 5. 6. x= Triangle: ___________ x= 7. A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. AB = _______ BC = _______ AC = _______ slope AB = ____ slope BC = ____ slope AC = ____ Therefore ABC is a _______________ triangle and IS / ISN’T a right triangle. Triangle: _________ A (3, 3), B (6, 9) , C (6, -3) 8. Find the measure of the exterior angle. #9-14 Find the measure of the numbered angle. 9. m 1= 12. m 2 = 10. m 3 = 13. m 4 = 11. m 5 = 14. m 6 = 15. PROVE: Exterior Angle Theorem Given: 1 is an exterior angle of ABC 1 Prove: m 1 = m A + m B Statements 1. 1 is an exterior angle Reasons 1. Given 2. ACB and 1 are a linear pair 2. 3. 3. Linear Pair Postulate 4. m ACB + m 1 = 180° 4. 5. m A + m B + m C = 180° 5. 6. m ACB + m 1 = m A + m B + m C 6. 7. m ACB = m C 7. 8. m ACB + m 1 = m A + m B + m ACB 8. 9. 9. Find the measure of each angle. 16. In ABC, mA = mB + 30° and mC = mB + 60°. Find the measure of each angle. 17. In ABC, mA = 2(mB) and mC = 3(mB). Find the measure of each angle. Find the values of x and y. 18. Hint: what special pair of angles is formed by the parallel lines? 19. 20.