Name: Class: Date: Geometry--Unit 3 Study Guide Determine the slope of the line that contains the given points. Refer to the figure below. 1 TÊ Á 6, 3 ˆ, V Ê Á 8, 8 ˆ A 2 5 B 5 2 C 0 D 2 5 Solve the system of equations. 2 x 5y = 2 2x 9y = 6 Find the measurement of the segment. 3 QT = 0.51 in., QV = 1.95 in. TV =? 4 Name all segments skew to GF. A AD, AB, BC, CD B BC, AD, DI, CH C FI, GH, DI, CH D CD, CH, DI, HI 5 Name all planes intersecting plane BAF. A BGH, CDA, FID, DIH B BCD, CHG, FID, FIH C DCH, DAF, CBG, CBA D BCH, GFI, FGH, CBG 6 Name all segments skew to HI. A AD, AB, BC, CD B FI, GH, DI, CH C BA, BG, AF, FG D BC, AD, AF, BG 7 Name all segments parallel to BG. A AF, DI, CH B BA, FG, GH, BC C GH, AD, FI D AD, CD, HI, FI 1
Name: 8 Name all planes intersecting plane CHG. A CDA, DAF, FGH, GBA B CBA, CDI, FIH, BAF C BAD, CDI, FID, BGF D ADC, DIH, FIH, CHI Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. 9 LHK HKN A B C D c Ä d ; congruent alternate interior angles a Ä b; congruent alternate interior angles c Ä d ; congruent corresponding angles a Ä b; congruent corresponding angles 2
Name: 10 2 6 A B C D a Ä b; congruent alternate exterior angles c Ä d ; congruent alternate exterior angles c Ä d ; congruent corresponding angles a Ä b; congruent corresponding angles 11 In the figure, p Ä q. Find m 1. Complete the sentence. 13 55 m? yd 100 cm = 1 m; 3 ft = 1 yd; 2.5 cm = 1 in; 10 dm = 1 cm A 59.7 B 62.3 C 60.5 D 61.7 14 7x 32 12 In the figure, m 1 = 70. Find m 2. Write an equation in point-slope form of the line having the given slope that contains the given point. 15 m = 3, Ê Á 2, 1ˆ A y + 2 = 3(x 1) B y 3 = 2(x 1) C y = 3x + 3 D y 1 = 3(x + 2) 3
Name: 16 Carpenters use parallel wall studs to build support for walls. A carpenter has built two wall studs given by HG and CD in the figure below. Find the measure of BDC so that the two wall studs are parallel. 19 In the figure, AB Ä CD. Find x and y. Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. 17 Given: segments RT and ST; twice the measure of ST is equalto the measure of RT. Conjecture: S is the midpoint of segment RT. A False; point S may not be on RT. B False; ST could be the segment bisector of RT. C False; lines do not have midpoints. D True 20 Nathan has a rectangular sheet of paper. He cut the sheet along the marked line. Find the measure of P. 18 Given: Conjecture: BCA BAC A False; the angles are not vertical. B True C False; the angles are not complementary. D False; there is no indication of the measures of the angles. 4
Name: Use the Distance Formula to find the distance between each pair of points. 23 In the figure, m RPZ = 95 and TU Find the measure of angle UZP. Ä RQ Ä VW. 21 24 In the figure, m NML = 120, PQ KL Ä TU and Ä NM. Find the measure of angle QSN. A 34 B 1 C 6 D 50 22 Write an equation in slope-intercept form of the line joining the points AÊ Á 10, 50ˆ and BÊ Á10, 30ˆ. Determine whether WX and YZ 25 WÊ Á 2, 6 ˆ, X Ê Á4, 2ˆ, Y Ê Á0, 4ˆ, Z Ê Á 1, 4 ˆ A neither B parallel C perpendicular are parallel, perpendicular, or neither. 5
Geometry--Unit 3 Study Guide Answer Section 1 B Ê Á y 2 y 1 ˆ The formula for slope is Ê Á x 2 x 1 ˆ. 2 Ê Á12, 2ˆ 2Ê Á2 + 5yˆ 9y = 6 4 + 10y 9y = 6 y = 2 x 5( 2) = 2 x 10 = 2 x = 12 3 1.44 in. TV is the length of QV minus the length of QT. 4 B Skew lines do not intersect and are not coplanar. 5 B Planes intersect in a line. 6 D Skew lines do not intersect and are not coplanar. 7 A Coplanar segments that do not intersect are parallel. 8 B Planes intersect in a line. 9 B Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If two lines are perpendicular to the same line, then lines are parallel. 1
10 D Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If two lines are perpendicular to the same line, then lines are parallel. 11 m 1 = 58 Extend v to intersect with p. This creates a linear pair at point S with angles measuring 111 (given) and 69. The angles formed by the intersection of v and p (also linear pairs) measure 127 (corresponding angles) and 53 with the latter being one of the interior angles of the triangle formed by t, p, and v. Since the sum of the angles of a triangle is 180, the angle that is vertical to 1 is 58, thus making 1 58 as well. 12 110 1 and 2 form a pair of consecutive interior angles and are thus supplementary. Therefore, 1 + 2 = 180. 13 C 14 14x 8 7x 32 7x 2 2 2 2 2 7x 4 2 2 2 14x 8 15 D The point-slope form is y y 1 = mê Á x x ˆ. Point Ê x, y 1 Á ˆ is a point through which the line passes. 1 1 16 82 The two wall studs will be parallel if BDC and the angle measuring 98 form a pair of consecutive interior angles and are thus supplementary. Therefore, BDC + 98 = 180. 17 A Even though they have a common point, the two segments do not have to be on the same line. 18 D Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent. 2
19 x = 49, y = 142 Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent. 20 95 P and the angle measuring 85 form a pair of consecutive interior angles and are thus supplementary. Therefore, P + 85 = 180. 21 A The Distance Formula is d = Ê Áx 2 x 1 ˆ 2 + Ê Á y 2 y 1 ˆ 2. 22 y = 4x + 10 The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. Use the point-slope form and either point to write the equation. y y 1 = mê Á x x ˆ, Ê x, y 1 Á ˆ are the coordinates of any point on the line and m = y y 2 1 is the slope of the line. 1 1 x 2 x 1 23 95 Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent. 24 60 Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent. 25 A Ê Á y 2 y 1 ˆ The formula for slope is Ê. If the slopes are the same they are parallel. If the product of the two slopes is Á x 2 x 1 ˆ 1, they are perpendicular. 3