Pre-Test. Name Date. List the side lengths from shortest to longest. 3. Explain how to construct a triangle given two line segments.

Transcription

1 Pre-Test Name Date List the side lengths from shortest to longest a 48 b c d 30 f 28 e 3. Explain how to construct a triangle given two line segments. 4. Explain why triangles constructed from the same two line segments are not necessarily congruent. Chapter 10 Assessments 1191

2 Pre-Test page 2 5. Triangle HIJ is congruent to nlmn. The measure of /H is 32, the measure of /I is 62, and the measure of /J is 86. What are m/l, m/m, and m/n? Explain your reasoning. 6. Figure ABCD is congruent to figure EFGH. Write the corresponding sides and corresponding angles that are congruent. 7. Larry constructed a triangle that is congruent to nqrs. To make sure the new triangle is congruent to nqrs, he used /R, /S, and the included side. Name the side that Larry used to construct the new triangle. Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning in., 8.9 in., 13.7 in m, 4 m, 10.9 m You are given the length of two sides of a triangle. What can you conclude about the length of the third side? in., 12 in mm, 153 mm 1192 Chapter 10 Assessments

3 Post-Test Name Date List the side lengths from shortest to longest c b 52 a d 112 f 33 e Explain how to construct a triangle given three angles. 4. Explain why triangles constructed from the same three angles are not necessarily congruent. Chapter 10 Assessments 1193

4 Post-Test page 2 5. Triangle DEF is congruent to nghi. The measure of /D is 41, the measure of /E is 39, and the measure of /F is 100. What are m/g, m/h, and m/i? Explain your reasoning. 6. Figure KLMN is congruent to figure OPQR. Write the corresponding sides and corresponding angles that are congruent. 7. Kevin constructed a triangle that is congruent to nfgh. To make sure the new triangle is congruent to nfgh, he used /G, /H, and the included side. Name the side that Kevin used to construct the new triangle. Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning in., 8.7 in., 15.4 in m, 5 m, 18.9 m You are given the length of two sides of a triangle. What can you conclude about the length of the third side? in., 9 in mm, 138 mm 1194 Chapter 10 Assessments

5 End of Chapter Test Name Date Solve for x. 1. x x 3. x x x + 14 Chapter 10 Assessments 1195

6 End of Chapter Test page 2 5. The measures of three interior angles of a triangle are 53, 47, and 80. Describe the location of each side with respect to the measure of the opposite interior angles without drawing or measuring any part of the triangle. a. longest side of the triangle b. shortest side of the triangle 6. Danielle and Jason each construct a triangle using two line segments shown. Will their triangles be congruent? Explain your reasoning. 7. Explain how to construct a triangle given three angles. 8. Philippe cuts the following three figures out of wood. A B F G J K C L E D I H N M a. Which two figures appear to be congruent? b. List the pairs of congruent line segments from the figures you named in part (a). c. List the pairs of congruent angles from the figures you named in part (a) Chapter 10 Assessments

7 End of Chapter Test page 3 Name Date 9. Ian, Isabella, Lloyd, and Jason made claims about triangles. Evaluate each of their claims. If one of the claims is false, give an example that disproves the claim. a. Ian says that if the three sides of one triangle have the same length as the three sides of a second triangle, then the two triangles are congruent. b. Isabella says if two sides and their included angle on one triangle have the same measures as two sides and their included angle on another triangle, then the two triangles are congruent. c. Lloyd says that if two angles and their included side on one triangle have the same measures as two angles and their included side on another triangle, then the two triangles are congruent. d. Jason says that if the three angles on one triangle have the same measure as the three angles on another triangle, then the triangles are congruent. Determine whether it is possible to form a triangle using the set of segments with the given measurements. Explain your reasoning in., 3.1 in., 7.2 in m, 8.4 m, 17 m Chapter 10 Assessments 1197

8 End of Chapter Test page mm, 97 mm, 92 mm yd, 35.6 yd, 19.2 yd You are given the length of two sides of a triangle. What can you conclude about the length of the third side? cm, 15 cm in., 4 in yd, 24 yd 17. Janet places a ladder against her house to clean the gutters, leaving 4 feet between the edge of the house and the ladder. The gutters are 15 feet off the ground. Using the Triangle Inequality Theorem, determine the range of heights her ladder should have Chapter 10 Assessments

9 Standardized Test Practice Name Date 1. You can construct congruent triangles if you know which of the following? a. the measures of two angles b. the measures of three angles c. the measures of two sides d. the measures of three sides 2. The lengths of two sides of a triangle are 3 cm and 7 cm. What can you conclude about the maximum length of the third side of the triangle? a. The maximum length of the third side must equal 10 cm. b. The maximum length of the third side must be greater than 10 cm. c. The maximum length of the third side must be less than 10 cm. d. The maximum length of the third side must equal 4 cm. 3. Which lists the side lengths in order from shortest to longest? d 73 e f 48 a. d, e, f b. d, f, e c. f, d, e d. f, e, d 4. Mary constructed njkl from two angles and their included side. The angles were /JKL and /KLJ. What was the included side? a. JK b. KJ c. JL d. LK Chapter 10 Assessments 1199

10 Standardized Test Practice page 2 5. Which describes how to construct a triangle given one line segment and two angles? a. Draw a starter ray; duplicate the line segment on the ray; duplicate each angle using the two endpoints of the line segment as vertices of the angles; extend the sides of the angles to form a triangle. b. Draw a starter line; locate point A on the starter line; duplicate /A at the point on the starter line; locate point B on the starter line; duplicate /B at the point on the starter line; duplicate /C using a side of /B; make sure all the sides of the triangle connect. c. Draw a starter line; locate point A on the starter line; duplicate AB on the starter line to locate point B; using point A as the endpoint, cut an arc duplicating AC ; label any point on the arc C; connect points A, B, and C to form nabc. d. Draw a starter line; draw an arc with center A that intersects both sides of the angle; using the same radius, draw an arc with center C; label points B, D, and E; draw an arc with radius BD at center E; label the intersection F; extend the sides of the angles to form a triangle. 6. Which theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side? a. Triangle Sum Theorem b. Triangle Inequality Theorem c. Exterior Angle Inequality Theorem d. Exterior Angle Theorem 7. A triangle has angle measures 23 and 35. What is the measure of the third angle? a. 32 b. 90 c. 122 d Figure GHIJ is congruent to figure NOPQ. What pair of angles must be congruent? a. /H and /P b. /J and /Q c. /I and /N d. /H and /Q 1200 Chapter 10 Assessments

11 Standardized Test Practice page 3 Name Date 9. The lengths of two sides of a triangle measure 9 feet and 21 feet. What is the smallest whole number value that the third side could measure? a. 9 feet b. 12 feet c. 13 feet d. 30 feet 10. What is the value of x? 114 2x x a. 38 b. 57 c. 76 d What is the measure of /ACD? A 33 a. 30 b. 63 c B C D d. 150 Chapter 10 Assessments 1201

12 Standardized Test Practice page Which of the following can be true for a pair of triangles that are not congruent? a. All corresponding sides are congruent. b. All corresponding angles are congruent. c. Two pairs of corresponding angles and their included sides are congruent. d. Two pairs of corresponding sides and their included angle are congruent. 13. The lengths of two sides of a triangle measure 8 feet and 14 feet. What is the largest whole number value that the third side could measure? a. 21 feet b. 22 feet c. 23 feet d. 24 feet 14. You can construct congruent triangles if you know which of the following? a. the measures of three sides b. the measures of two angles and one given side c. the measures of two sides and the included angle d. all of the above 15. Which theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle? a. Triangle Sum Theorem b. Remote Interior Angle Theorem c. Exterior Angle Theorem d. Exterior Inequality Theorem 16. A triangular bike path is exactly 9 miles long. If each of the three connecting paths is a whole-number of miles long, which could be the lengths of the paths? a. 1 mile, 1 mile, 7 miles b. 1 mile, 2 miles, 6 miles c. 2 miles, 2 miles, 5 miles d. 2 miles, 3 miles, 4 miles 1202 Chapter 10 Assessments

13 Standardized Test Practice page 5 Name Date 17. Figure WXYZ is congruent to figure ABCD. What pair of sides must be congruent? a. XY and AB b. XY and BC c. XY and CD d. XY and AD 18. In the two triangles shown, AB > ED, BC > DF, AC > EF, /A > /E, /B > /D, and /C > /F. Which congruency statement describes the relationship between the two triangles? A D B C F E a. nbac ndef b. nabc ndef c. ncab nedf d. nabc nedf 19. What can you conclude about /ACD using the Exterior Angle Inequality Theorem? A B C D a. the measure of /ACD is less than 121 b. the measure of /ACD is greater than 121 c. the measure of /ACD is less than the sum of 121 and 17 d. the measure of /ACD is greater than the sum of 121 and 17 Chapter 10 Assessments 1203

14 Standardized Test Practice page Tommy drew a triangle. Which information will enable you to draw a triangle that is congruent to Tommy s triangle? a. two given sides b. two given angles c. two given angles and one given side d. three given angles 1204 Chapter 10 Assessments