Geo - CH4 Practice Test
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1 Geo - H4 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify Δ by its side lengths. a. equilateral triangle c. scalene triangle b. isosceles triangle d. obtuse triangle 2. Two sides of an equilateral triangle measure (2y + 3) units and (y 2 5) units. If the perimeter of the triangle is 33 units, what is the value of y? a. y = 11 c. y = 4 b. y = 15 d. y = 7 3. Find m K. a. m K = 63 c. m K = 79 b. m K = 55 d. m K = Find m, given F, E, and m E = 46.
2 a. m = 134 c. m = 44 b. m = 67 d. m = What additional information do you need to prove Δ Δ by the SS Postulate? a. c. b. d. 6. Use S to prove the triangles congruent. Given: Ä GH, Ä FH, FH Prove: Δ ΔHGF omplete the flowchart proof. Proof: Ä GH G Given 1. Ä FH HFG Δ ΔHGF Given 2. S
3 Ä GH G Given 1. Ä FH HFG Δ ΔHGF Given 2. S FH Given a. 1. lternate Exterior ngles Theorem 2. lternate Interior ngles Theorem b. 1. lternate Interior ngles Theorem 2. lternate Exterior ngles Theorem c. 1. lternate Exterior ngles Theorem 2. lternate Exterior ngles Theorem d. 1. lternate Interior ngles Theorem 2. lternate Interior ngles Theorem 7. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. a. Δ ΔJLK, HL c. Δ ΔJLK, SS b. Δ ΔJKL, HL d. Δ ΔJKL, SS 8. Given: MLN PLO, MNL POL, MO NP Prove: ΔMLP is isosceles.
4 omplete the proof. Proof: Statements Reasons 1. MLN PLO, MNL POL 1. Given 2. MO NP 2. Given 3. MO = NP 3. efinition of congruent line segments 4. NO = NO 4. Reflexive Property of Equality 5. MO NO = NP NO 5. Subtraction Property of Equality 6. MO NO = MN and NP NO = OP 6. Segment ddition Postulate 7. MN = OP 7. Substitution Property of Equality 8. ΔMLN ΔPLO 8. [1] 9. ML PL 9. [2] 10. ΔMLP is isosceles. 10. efinition of isosceles triangle a. [1] PT c. [1] PT [2] S [2] S b. [1] S d. [1] S [2] PT [2] PT 9. Which of the following is not a positioning of a right triangle with leg lengths of 4 units and 5 units?
5 a. c. b. d. 10. Find m Q. a. m Q = 30 º c. m Q = 70 º b. m Q = 60 º d. m Q = 75 º 11. Find.
6 a. = 10 b. = 12 c. = 14 d. Not enough information. n equiangular triangle is not necessarily equilateral. Numeric Response 12. n isosceles triangle has a perimeter of 50 in. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is the value of x? 13. Find the value of x. Matching Match each vocabulary term with its definition. a. interior angle b. complementary angles c. supplementary angles d. exterior angle e. interior f. remote interior angle g. exterior
7 14. an angle formed by one side of a polygon and the extension of an adjacent side 15. an angle formed by two sides of a polygon with a common vertex 16. an interior angle of a polygon that is not adjacent to the exterior angle 17. the set of all points outside a polygon 18. the set of all points inside a polygon Match each vocabulary term with its definition. a. exterior angle b. corresponding angles c. interior angle d. included angle e. vertex angle f. included side g. corresponding sides 19. angles in the same relative position in two different polygons that have the same number of angles 20. the angle formed by the legs of a triangle 21. the common side of two consecutive angles of a polygon 22. sides in the same relative position in two different polygons that have the same number of sides 23. the angle formed by two adjacent sides of a polygon
8 Geo - H4 Practice Test nswer Section MULTIPLE HOIE 1. NS: From the figure. So, = 8, and Δ is equilateral. The measure of segment is also 8. What is the name of a triangle that has three congruent sides? scalene triangle has no congruent sides. n obtuse triangle has one obtuse angle. lassify the triangle by the side lengths, not the angle measures. PTS: 1 IF: asic REF: Page 217 OJ: lassifying Triangles by Side Lengths NT: f TOP: 4-1 lassifying Triangles 2. NS: The perimeter is 33 units and it is an equilateral triangle, so each side has length 11 units. Use this to solve for either side. 11 = 2y = 2y 4 = y 11 = y = y 2 4 = y n answer of 4 does not apply here. This is the length of each side. Now find the value of y. The perimeter is 33 so the length of each side is 11. Set one of the sides equal to 11 and solve for y. When solving 2y + 3 = 11, subtract 3 from both sides of the equation. PTS: 1 IF: dvanced NT: h TOP: 4-1 lassifying Triangles 3. NS: m K + m L = m LMN Exterior ngle Theorem ( 6x 9) + ( 4x + 7) = x 2 = x = 120 Substitute 6x 9 for m K, 4x + 7 for m L, and 118 for m LMN. Simplify. dd 2 to both sides.
9 x = 12 ivide both sides by 10. m K = 6x 9 = 6( 12) 9 = 63 You found the measure of angle L. Find the measure of angle K instead. First, use the Exterior ngle Theorem to find the value of x. Then substitute the value for x to find the measure of angle K. First, use the Exterior ngle Theorem to find the value of x. Then substitute the value for x to find the measure of angle K. PTS: 1 IF: verage REF: Page 225 OJ: pplying the Exterior ngle Theorem NT: f TOP: 4-2 ngle Relationships in Triangles 4. NS: The Third ngles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. It is given that F and E. Therefore, E. So, m = 46. This is the supplement. Use the Third ngles Theorem. The Third ngles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. This is the complement. Use the Third ngles Theorem. PTS: 1 IF: dvanced NT: f TOP: 4-2 ngle Relationships in Triangles 5. NS: The SS Postulate is used when two sides and an included angle of one triangle are congruent to the corresponding sides and included angle of a second triangle. From the given,. From the figure, by the Reflexive Property of ongruence. You have two pair of congruent sides, so you need information about the included angles. Use these pairs of sides to determine the included angles. The angle between sides and is. The angle between sides and is. You need to know to prove Δ Δ by the SS Postulate. This information is needed to use the SSS Postulate.
10 You need the included angle between the two sides. This information is already given. Find information that you need that is not given or true in the figure. PTS: 1 IF: dvanced NT: a TOP: 4-4 Triangle ongruence: SSS and SS 6. NS: 1. and G are alternate interior angles and Ä GH. Thus by the lternate Interior ngles Theorem, G. 2. and HFG are alternate exterior angles and ngles Theorem, HFG. Ä FH. Thus by the lternate Exterior You switched the definitions of alternate interior and alternate exterior angles. If line segment is parallel to line segment GH, are angle and angle G alternate exterior angles or alternate interior angles? If line is parallel to line FG, are angle and angle HFG alternate interior angles or alternate exterior angles? PTS: 1 IF: verage REF: Page 254 OJ: Using S to Prove Triangles ongruent NT: a TOP: 4-5 Triangle ongruence: S S and HL 7. NS: ecause and KJL are right angles, Δ and ΔJKL are right triangles. You are given a pair of congruent legs JL and a pair of congruent hypotenuses LK. So a hypotenuse and a leg of Δ are congruent to the corresponding hypotenuse and leg of ΔJKL. Δ ΔJKL by HL. Segment is congruent to segment JL. Make sure the triangle vertices correspond accordingly. Segment is congruent to segment JL. Make sure the triangle vertices correspond accordingly. For SS, the angle is included between the sides. For SS, the angle is included between the sides. PTS: 1 IF: dvanced NT: a TOP: 4-5 Triangle ongruence: S S and HL 8. NS: [1] Steps 1 and 7 state that two angles and a nonincluded side of ΔMLN and ΔPLO are congruent. y S, ΔMLN ΔPLO.
11 [2] Since ΔMLN ΔPLO, by PT, ML PL. efore using PT, you must prove that triangle MLN and triangle PLO are congruent. Since steps 1 and 7 state that two angles and a nonincluded side are congruent, which triangle congruence theorem states that the triangles are congruent? Steps 1 and 7 state that two angles and a nonincluded side of triangle MLN and triangle PLO are congruent. Which triangle congruence theorem states that the triangles are congruent? efore using PT, you must prove that triangle MLN and triangle PLO are congruent. PTS: 1 IF: verage REF: Page 261 OJ: Using PT in a Proof NT: a TOP: 4-6 Triangle ongruence: PT 9. NS: These graphs show right triangles with leg lengths of 4 units and 5 units with one vertex at the origin. This graph shows a right triangle with leg lengths of 4 units and 5 units with the base centered at the origin. This graph shows an isosceles triangle that is not a right triangle.
12 This is a right triangle with a vertex at the origin. This is a right triangle with a vertex at the origin. This is a right triangle with a vertex at the origin. PTS: 1 IF: asic REF: Page 267 OJ: Positioning a Figure in the oordinate Plane NT: d TOP: 4-7 Introduction to oordinate Proof 10. NS: m Q = m R = ( 2x + 15) Isosceles Triangle Theorem m P + m Q + m R = 180 Triangle Sum Theorem x + ( 2x + 15) + ( 2x + 15) = 180 Substitute x for m P and substitute 2x + 15 for m Q and m R. 5x = 150 Simplify and subtract 30 from both sides. x = 30 ivide both sides by 5. Thus m Q = ( 2x + 15) = [2( 30) + 15] = 75. This is x. The measure of angle Q is 2x y the Isosceles Triangle Theorem, the measure of angle Q equals the measure of angle R. Use the Triangle Sum Theorem and solve for x. y the Isosceles Triangle Theorem, the measure of angle Q equals the measure of angle R. Use the Triangle Sum Theorem and solve for x. PTS: 1 IF: verage REF: Page 274 OJ: Finding the Measure of an ngle TOP: 4-8 Isosceles and Equilateral Triangles NT: f
13 11. NS: Δ is equilateral. 2s 10 = s + 2 s = 12 Equiangular triangles are equilateral. efinition of equilateral triangle. Subtract s and add 10 to both sides of the equation. = 2s 10 = 2( 12) 10 Substitute 12 for s in the equation for. = 14 Simplify. = = 14 efinition of equilateral triangle. Substitute 14 for. Equiangular triangles are equilateral. Use = to solve for s, and then use = or = to find. This is s. Substitute s in the original equation to find. y a corollary to the Isosceles Triangle Theorem, equiangular triangles are equilateral. Use = to solve for s, and then use = or = to find. PTS: 1 IF: asic REF: Page 275 OJ: Using Properties of Equilateral Triangles TOP: 4-8 Isosceles and Equilateral Triangles NT: f NUMERI RESPONSE 12. NS: 5.5 PTS: 1 IF: dvanced NT: e TOP: 4-1 lassifying Triangles KEY: perimeter isosceles 13. NS: 21.6 PTS: 1 IF: verage NT: f TOP: 4-8 Isosceles and Equilateral Triangles KEY: equilateral equiangular MTHING 14. NS: PTS: 1 IF: asic REF: Page 225 TOP: 4-2 ngle Relationships in Triangles 15. NS: PTS: 1 IF: asic REF: Page 225 TOP: 4-2 ngle Relationships in Triangles 16. NS: F PTS: 1 IF: asic REF: Page 225
14 TOP: 4-2 ngle Relationships in Triangles 17. NS: G PTS: 1 IF: asic REF: Page 225 TOP: 4-2 ngle Relationships in Triangles 18. NS: E PTS: 1 IF: asic REF: Page 225 TOP: 4-2 ngle Relationships in Triangles 19. NS: PTS: 1 IF: asic REF: Page 231 TOP: 4-3 ongruent Triangles 20. NS: E PTS: 1 IF: asic REF: Page 273 TOP: 4-8 Isosceles and Equilateral Triangles 21. NS: F PTS: 1 IF: asic REF: Page 252 TOP: 4-5 Triangle ongruence: S S and HL 22. NS: G PTS: 1 IF: asic REF: Page 231 TOP: 4-3 ongruent Triangles 23. NS: PTS: 1 IF: asic REF: Page 242 TOP: 4-4 Triangle ongruence: SSS and SS
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