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Transcript
Honors Geometry Ch 4 Review Practice Name______________________________________#_______ Some practice proofs. DA bisects BAC Given: A. AD BC B C Show: A 1 3 2 4 D B B. Given: C FS // LG LS // AG L is the midpoint of FA LS AG Show: F L 3 S 2 A C. G H and N are right angles Given: DO OU HD NU Show: U H D O 2 1 N All of the following statements are false. Correct them to make them true. 1. The sum of the measures of the angles in an obtuse triangle is greater than the sum of the measures of the angles in scalene triangle. 2. In an isosceles triangle, if the measure of one base angle is 45 degrees, then the triangle must be an acute triangle. 3. In right scalene triangle ABC with right angle B, if 𝒎∠𝑨 = 𝟔𝟕° then ̅̅̅̅ 𝑩𝑪 is the shortest side. 4. If a triangle has two 30 degree angles, then it is an acute isosceles triangle. 5. If the measure of an exterior angle of a triangle is twice its linear pair, then the sum of the two remote interior angles is 90 degrees. 6. If two sides of one triangle are congruent to two sides of another triangle then the triangles must be congruent. 7. Only one triangle can be constructed from two sides and a non-included angle. 8. In a right triangle, the bisector of the right angle is also an altitude. 9. Every equilateral triangle is equiangular, but not every equiangular triangle is equilateral. 10. CPCTC stands for Congruent Parts of Congruent Triangles are Corresponding. 11. If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the segment. 12. If two parallel lines are cut by a transversal, then the consecutive interior angles are congruent. 13. If two lines do not intersect, they must be parallel. 14. Deductive reasoning involves recognizing patterns. 15. You use a ruler and a protractor to do geometric constructions. 16. In triangle XYZ, if 𝒎∠𝑿 = 𝟑𝟓° 𝒂𝒏𝒅 𝒎∠𝒁 = 𝟏𝟎𝟎°, list the sides in order from shortest to longest. 1. Given WER CHS , complete the congruence statements: SC ________ EW ________ H ________ ER ________ C ________ R ________ 2. Determine if the given lengths can create a triangle. You must show why or why not. a.) 81 47 , , 27 4 4 b.) c.) 26 1 , 4, 10 5 5 15, 9, 24 5. If two sides of a triangle measure 78 cm and 31 cm, between what two numbers must the measure of the 3rd side fall? 6. Given RED where mR 141 , mE 30 , mD 9 , list the sides of the triangle from longest to shortest. 8. The perimeter of the triangle is 142 cm, find all the missing measures in the diagram. 7. Given BLU where BL 19 cm , LU 65 cm , BU 48 cm , list the angles of the triangle from the smallest to largest. Solve for variable(s) in each picture. 9. ________ 10. ________ 11. ________ ◦ (x+5) ◦ (3x - 10) ◦ (115) 12. ________ 13. ________ 14. ________ 15. ________ 16. ________ 17. ________ 18. ________ 19. ________ & ________ 20. ________ 21. TRY GEO , mT 36 , mE 73 , Find mO . 22. Given: ABC XYZ, AB 38 , YZ 28 , and XY 5x 8 . Solve for x . (Hint: Draw a picture.) 23. Given an isosceles triangle with vertex angle that measures 70, what is the measure of a base angle? 24. 25. Given: ABC is isosceles with vertex C. If mA 3x 6 and mC 2 x . Solve for x and find mB . (Hint: Draw a picture.) ABC is an isosceles triangle with vertex angle B. AB = 5x – 28, AC = x+ 5, and BC = 2x + 11. Solve for x and find the length of the base. (Hint: Draw a picture.) Determine if the given triangles are congruent. If yes, state the reason why. 26. ________ 27. ________ 28. ________ 29. ________ 30. ________ 31. ________ 32. ________ 33. ________ 34. Construct triangle ABC given the following side and angles: • A • B A B 35. Construct the incenter of the triangle below.