Test Review: Geometry I Period 3/5/7 Test Date: Period 3: Friday December 19 Period 5/7: Monday December 22

Transcription

1 Test Review: Geometry I Period 3/5/7 Test ate: Period 3: Friday ecember 19 Period 5/7: Monday ecember 22 Things it would be a good idea to know: 1) ifferent types of triangles 2) Use lgebra to find the measures of angles and name them properly 3) ll Theorems and Postulates 4) How to prove two triangles congruent by SSS, SS, S, S and HL 5) How to use congruent triangles to prove angles congruent, segments congruent, lines parallel or perpendicular. 6) 4 types of transformations and which are isometric. Test Outline Part I. Part II. Part III Part IV Multiple hoice & True False 10 Questions (20pts) Using lgebra to classify triangles 4 problems (20pts) Transformations 1 problem (10pts) 5 Proofs (50pts) ttached are practice problems

2 1) GIVEN: E E PROVE: E

3 2) Given: is isosceles is isosceles Prove: bisects

4 3) Given: EF, EF, EG Prove: G E F G

5 4) Given: ; Prove:

6 5) Given:,, Prove: E is isosceles E

7 6) Given: FG FJ HG IJ Prove: FHI FIH F G H I J

8 7) Given: G G Prove: G G

9 8) Given: ML PL, PNK MKN Prove: MN PK M P L N K

10 9) Given:, E Prove: E E

11 10) Given: = EF; E ; E E ; F Prove: F E F

12 NME TE PERIO 4 hapter 4 Test, Form 2 SORE 1. Use a protractor and ruler to classify the triangle by its angles and sides Find x,,, and if is equilateral x - 6 7x + 3 8x 3. Find the measure of the sides of the triangle if the vertices of EFG are E(-3, 3), F(1, -1), and G(-3, -5). Then classify the triangle by its sides. 3. Use the figure for Question 4-6. Find the measure of each angle. opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. 4. m 1 5. m 2 6. m 3 7. Identify the congruent triangles and name their corresponding congruent angles. 8. Identify the transformation and verify that it is a congruence transformation G y 1 F 3 x ssessment hapter 4 67 Glencoe Geometry

13 NME TE PERIO 4 hapter 4 Test, Form 2 (continued) 9. rectangular piece of paper measuring 8 inches by 16 inches is folded in half to form a square. It is then folded again along its diagonal to form a triangle. Find the measures of the angles of the triangle KLM is an isosceles triangle and 1 2. Name the theorem that could be used to determine LKP LMN. Then name the postulate that could be used to prove LKP LMN. hoose from SSS, SS, S, and S. K L 1 2 P N M Find m Find the value of x. (18x - 12) x (10x + 20) 13. Position and label isosceles with base, b units long, on the coordinate plane. 14. P joins point in isosceles right to the midpoint P, of. Name the coordinates of P. Then determine the relationship between and P. onus Without finding any other angles or sides congruent, determine which pair of triangles can be proved to be congruent by the HL Theorem. E Y N y (0, b) P (0, 0) (b, 0) x : opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. F X Z M O hapter 4 68 Glencoe Geometry

14 NME TE PERIO 4 hapter 4 Test, Form 2 SORE 1. Use a protractor and ruler to classify the triangle by its angles and sides Find x,,, if is isosceles with =. 5x + 5 2x x Find the measure of the sides of the triangle if the vertices of EFG are E(1, 4), F(5, 1), and G(2, -3). Then classify the triangle by its sides. 3. Use the figure for Questions 4-6. Find the measure of each angle. 4. m opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. 5. m 2 6. m 3 7. Identify the congruent triangles and name their corresponding congruent angles. 8. Identify the transformation and verify that it is a congruence transformation. E y x F ssessment 9. square piece of paper measuring 8 inches on each side is folded in half forming a triangle. It is then folded in half again to form another triangle. Find the angles of the resulting triangle. 9. hapter 4 69 Glencoe Geometry

15 NME TE PERIO 4 hapter 4 Test, Form 2 (continued) 10. is an isosceles triangle with. Name the theorem that could be used to determine. Then name the postulate that could be used to prove. hoose from SSS, SS, S, and S Find m Find the value of x. (18x - 8) 12. (6x + 4) 13. Position and label equilateral KLM with side lengths 3a units long on the coordinate plane MN joins the midpoint of and the midpoint of in. Find the coordinates of M and N. (0, b) N(?,?) (0, 0) onus Without finding any other angles or sides congruent, determine which pair of triangles can be proved to be congruent by the LL Theorem. y M(?,?) (a, 0) x 14. : opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. E Y N F X Z M O hapter 4 70 Glencoe Geometry

16 NME TE PERIO 4 hapter 4 Test, Form 3 SORE 1. If is isosceles, is the vertex angle, = 20x - 2, = 12x + 30, and = 25x, find x and the length of each side of the triangle Find the length of the sides of the triangle with vertices (0, 4), (5, 4), and (-3, -2). lassify the triangle by its sides and angles. 2. Use the figure to answer Questions (3x - 10) (8x - 30) 3. Find the value of x. 3. opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. 4. Find m 1, if m 1 = 4x Find m The vertices of are (-1, 1), (4, 2), and (1, 5). The vertices of EF are (-1, -1), E(4, -2), and F(1, -5) so that EF. Identify the congruence transformation. 7. etermine whether GHI JKL, given G(1, 2), H(5, 4), I(3, 6) and J(-4, -5), K(0, -3), L(-2, -1). Explain. 8. In the figure, F, E, and F. etermine which postulate can be used to prove EF. hoose from SSS, SS, S, and S. F E ssessment hapter 4 71 Glencoe Geometry

17 NME TE PERIO 4 hapter 4 Test, Form 3 (continued) For Questions 9 and 10, complete this two-column proof. Given: is an isosceles triangle with base. is the midpoint of. Prove: bisects 1 2 Proof: Statements 1. is isosceles with base. 2. Reasons 1. Given 2. ef. of isosceles triangle (Question 9) 4. is the midpoint of. 4. Given Midpoint Theorem (Question 10) PT 8. bisects 8. ef. of angle bisector Find x. 12. Position and label isosceles with base, (a + b) units long, on a coordinate plane 13. wood column is supported by four cables that form four triangles. etermine which postulate can be used to show that all the triangles are congruent. onus In the figure, is isosceles, is equilateral, E is isosceles, and the measures of 9, 1, and 3 are all equal. Find the measures of the nine numbered angles E 4 5 (21x - 3) 6 8 (17x + 9) (15x + 15) : opyright Glencoe/McGraw-Hill, a division of The McGraw-Hill ompanies, Inc. hapter 4 72 Glencoe Geometry