Midterm Review Name. 2. Line l intersects lines w, x, y, and z. Which two lines are parallel? o w. 70 o. 100 o. 110 o
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1 Midterm Review Name 1. In the figure, lines l and m are cut by the transversal t forming the angles shown. Name all corresponding, alternate interior, alternate exterior, consecutive interior, vertical and linear pair angles. t l m 2. Line l intersects lines w, x, y, and z. Which two lines are parallel? o w 70 o x l 100 o 110 o y z
2 3. Lines and CD intersect at P. PR is perpendicular to, and m PD = 160 degrees. What is the measure of DP? Explain your reasoning. R D C P 4. This diagram shows how a periscope works. If the two mirrors are parallel and 1 3, what is m 6 when m 2 = 80 degrees? (Dotted lines a, b are parallel) Explain your reasoning. a mirror 4 5 b mirror 6
3 5. Lookout towers are located at points,, and C on the section of a national forest shown in the drawing. Which of the following statements is true concerning C formed by the towers? 4,123 m 5,385 m 4,472 m a. m C is the greatest b. m is the least c. m is the greatest m C is the least 6. From a point 22 feet from the base of a tower, a wire is stretched to an attachment 44 feet up the tower. To the nearest foot, how long is the wire? 44 feet 22feet
4 7. Triangles C and EFG are similar with measurements shown. What is the ratio of C? EG C G E F 8. Three boats are anchored in a bay. Given the information in the diagram, which of the following statements concerning the distances between the boats is true?. C <. C < C. < C D. C < C 61 o C 71 o 9. Given the endpoints (-3,5) and (7,-2) find the midpoint. 10. Given the midpoint (-2,6) and then endpoint (4,-2) find the other endpoint.
5 11. On the shores of a river, surveyors marked locations, and C. The measure of C = 40 degrees and the measure of C = 105 degrees. Which lists the distances between these locations in order, least to greatest? Explain your reasoning. C a. to, to C, to C b. to C, to C, to c. to C, to, to C d. to C, to, to C 12. Name three side lengths that could make a triangle. Explain your reasoning. 13. Name three side lengths that could not make a triangle. Explain your reasoning 14. Find the length of the third side of the right triangle with a hypotenuse of 10 and one leg of 6.
6 15. Three towns form a triangle on a map. The angle formed at the point designating fton is 42 degrees, a adenton 45 degrees and at Capeton 93 degrees. Which lists the distances between the towns from greatest to least? Capeton fton adenton fton to adenton, adenton to Capeton, fton to Capeton fton to adenton, fton to Capeton, adenton to Capeton C fton to Capeton, fton to adenton, adenton to Capeton D adenton to Capeton, fton to adenton, fton To Capeton 16. What is the m 3? 3 Capeton 40 degrees 145 degrees 17. Write the inverse, converse and contrapositive of the conditional statement, If an angle is a right angle, then it measures 90 degrees.
7 18. Given: C DC D C Which could be used to prove D CD?. SSS If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.. SS If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them in another triangle, then the triangles are congruent. C. S If 2 angles and the side of one triangle are congruent to 2 angles and the of another triangle then the 2 triangles are congruent. D. S If 2 angles and a side not between them are congruent to 2 angles and a side not between them of another triangle, then the triangles are congruent. D 19. What is the slope of a line through (-4, 8) (7, -5)? 20. What is the other endpoint given the midpoint (-3, 6) and endpoint (2, -4)? 21. If a right triangle has legs that measure 6 in and 8 in, what is the length of the hypotenuse? Make a conclusion based on the following true statements: If today is Wednesday, then I will go to tutoring. If I go to tutoring, then I get extra credit.
8 23 n airplane is 35 miles from the end of the runway (G) and 6 miles high (PG) when it begins its approach to the airport. To the nearest mile, what is the distance (P) from the airplane to the end of the runway? P G 24. The figure has angle measures as shown. What is the measure of the exterior angle? 7x + 5 4x 4x 25. Find the slope of the line containing the two points (-3, 7) and (4, -5). 26. Write the contrapositive. If two angles are vertical angles then they are congruent.
9 27. painter rests his ladder against a shed. The ladder made a 45 o angle with the ground as shown in the diagram below. Which angle or angles represent the supplement to the 45 o angle? w x z 45 o 28. n airplane leaves a runway heading due east then turns 34 o to the right as shown in the figure. How much more will the airplane have to turn to be heading due south? 34 o 29. What is m 3? 25 o o 30. Solve for x. 3x+10 2x+120 3x+10
10 Midterm Vocabulary Terms Please review the following vocabulary words. collinear coplanar midpoint segment bisector angle bisector perpendicular lines parallel lines slope skew lines transversal hypotenuse right angle acute angle obtuse angle adjacent angle vertical angles supplementary angles complementary angles exterior angle of a triangle consecutive interior angles symmetric property reflexive property transititve property substitution property law of detachment law of syllogism acute triangle obtuse triangle right triangle equiangular triangle scalene triangle isosceles triangle equilateral triangle altitude of a triangle median of a triangle angle bisector of a triangle perpendicular bisector of a triangle Know the following symbols/ formulas congruent equal not equal greater than less than parallel perpendicular triangle angle measure of angle distance formula midpoint formula slope formula
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