Perpendicular and Angle Bisectors Quiz
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1 Name: lass: ate: I: Perpendicular and ngle isectors Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measures and. a. = 6.4, = 4.6 b. = 4.6, = 6.4 c. = 6.4, = 2. d. = 2., = Given that YW bisects XYZ and WZ = 4.2, find WX. a. WX = 4.2 b. WX = 8.46 c. WX = 45 d. WX = 90. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints ( 2,2) and (5,4). a. y = 7 (x 1.5) 2 b. y = 2 (x 1.5) 7 c. y 1 = 2 (x.5) 7 d. y 1 = 7 (x.5) 2 1
2 I: Perpendicular and ngle isectors Quiz nswer Section MULTIPLE HOIE 1. NS: = = 6.4 X = X X = 2. = X + X = = 4.6 Perpendicular isector Theorem Substitute 6.4 for. Given Segment ddition Postulate Simplify. Switch the answers for and. is twice X. Switch the answers for and. is twice X. PTS: 1 IF: verage REF: 1acdb6d df-9c7d f0d2ea OJ: pplying the Perpendicular isector Theorem and Its onverse ST: NY.NYLES.MTH.05.GEO.G.G.49.a LO: MTH MTH OK: OK 2 2. NS: WX = WZ WX = 4.2 ngle isector Theorem KEY: perpendicular bisector PTS: 1 IF: asic REF: 1acff21e df-9c7d f0d2ea OJ: pplying the ngle isector Theorems LO: MTH KEY: angle bisector OK: OK 1 1
3 I:. NS: Step 1 Plot. The perpendicular bisector of is perpendicular to at its midpoint. Step 2 Find the midpoint of. Ê Midpoint of = 2 + 5, ˆ Ë Á 2 2 = (1.5,) Step Find the slope of the perpendicular bisector. (4) (2) Slope of = (5) ( 2) = 2 7 Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is 7 2. Step 4 Use point-slope form to write the equation. y y 1 = m(x x 1 ) y = 7 (x 1.5) 2 The perpendicular bisector has a slope that is perpendicular to the given segment. To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. The perpendicular bisector has a slope that is perpendicular to the given segment. To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. PTS: 1 IF: verage REF: 1ad27b8a df-9c7d f0d2ea OJ: Writing Equations of isectors in the oordinate Plane NT: NT.SS.MTH G.GPE.5 ST: NY.NYLES.MTH.05.GEO.G.G.49.a NY.NYLES.MTH.05.GEO.G.G.68 LO: MTH MTH KEY: point-slope form perpendicular bisector coordinate geometry 2
4 I: OK: OK 2
5 Name: lass: ate: I: Perpendicular and ngle isectors Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measures and. a. = 6.4, = 2. b. = 6.4, = 4.6 c. = 2., = 6.4 d. = 4.6, = Given that YW bisects XYZ and WZ = 4.2, find WX. a. WX = 90 b. WX = 45 c. WX = 8.46 d. WX = 4.2. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints (2,2) and (6,5). a. y 1.5 = (x 2) 4 b. y.5 = 4 (x 4) c. y.5 = (x 4) 4 d. y 1.5 = 4 (x 2) 1
6 I: Perpendicular and ngle isectors Quiz nswer Section MULTIPLE HOIE 1. NS: = = 6.4 X = X X = 2. = X + X = = 4.6 Perpendicular isector Theorem Substitute 6.4 for. Given Segment ddition Postulate Simplify. is twice X. Switch the answers for and. is twice X. Switch the answers for and. PTS: 1 IF: verage REF: 1acdb6d df-9c7d f0d2ea OJ: pplying the Perpendicular isector Theorem and Its onverse ST: NY.NYLES.MTH.05.GEO.G.G.49.a LO: MTH MTH OK: OK 2 2. NS: WX = WZ WX = 4.2 ngle isector Theorem KEY: perpendicular bisector PTS: 1 IF: asic REF: 1acff21e df-9c7d f0d2ea OJ: pplying the ngle isector Theorems LO: MTH KEY: angle bisector OK: OK 1 1
7 I:. NS: Step 1 Plot. The perpendicular bisector of is perpendicular to at its midpoint. Step 2 Find the midpoint of. Ê Midpoint of = , ˆ Ë Á 2 = (4,.5) Step Find the slope of the perpendicular bisector. (5) (2) Slope of = (6) (2) = 4 Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is 4. Step 4 Use point-slope form to write the equation. y y 1 = m(x x 1 ) y.5 = 4 (x 4) To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. The perpendicular bisector has a slope that is perpendicular to the given segment. The perpendicular bisector has a slope that is perpendicular to the given segment. To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. PTS: 1 IF: verage REF: 1ad27b8a df-9c7d f0d2ea OJ: Writing Equations of isectors in the oordinate Plane NT: NT.SS.MTH G.GPE.5 ST: NY.NYLES.MTH.05.GEO.G.G.49.a NY.NYLES.MTH.05.GEO.G.G.68 LO: MTH MTH KEY: point-slope form perpendicular bisector coordinate geometry 2
8 I: OK: OK 2
9 Name: lass: ate: I: Perpendicular and ngle isectors Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given that YW bisects XYZ and WZ = 4.2, find WX. a. WX = 8.46 b. WX = 45 c. WX = 90 d. WX = Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints ( 2,2) and (,5). a. y 1.5 = (x 2.5) 5 b. y 1.5 = 5 (x 2.5) c. y.5 = 5 (x 0.5) d. y.5 = (x 0.5) 5. Find the measures and. a. = 4.6, = 6.4 b. = 6.4, = 4.6 c. = 2., = 6.4 d. = 6.4, = 2. 1
10 I: Perpendicular and ngle isectors Quiz nswer Section MULTIPLE HOIE 1. NS: WX = WZ WX = 4.2 ngle isector Theorem PTS: 1 IF: asic REF: 1acff21e df-9c7d f0d2ea OJ: pplying the ngle isector Theorems LO: MTH KEY: angle bisector OK: OK 1 1
11 I: 2. NS: Step 1 Plot. The perpendicular bisector of is perpendicular to at its midpoint. Step 2 Find the midpoint of. Ê Midpoint of = 2 +, ˆ Ë Á 2 2 = (0.5,.5) Step Find the slope of the perpendicular bisector. (5) (2) Slope of = () ( 2) = 5 Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is 5. Step 4 Use point-slope form to write the equation. y y 1 = m(x x 1 ) y.5 = 5 (x 0.5) To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. The perpendicular bisector has a slope that is perpendicular to the given segment. To find the midpoint, add the x-coordinates and divide by 2, and add the y-coordinates and divide by 2. The perpendicular bisector has a slope that is perpendicular to the given segment. PTS: 1 IF: verage REF: 1ad27b8a df-9c7d f0d2ea OJ: Writing Equations of isectors in the oordinate Plane NT: NT.SS.MTH G.GPE.5 ST: NY.NYLES.MTH.05.GEO.G.G.49.a NY.NYLES.MTH.05.GEO.G.G.68 LO: MTH MTH KEY: point-slope form perpendicular bisector coordinate geometry 2
12 I: OK: OK 2. NS: = = 6.4 X = X X = 2. = X + X = = 4.6 Perpendicular isector Theorem Substitute 6.4 for. Given Segment ddition Postulate Simplify. Switch the answers for and. Switch the answers for and. is twice X. is twice X. PTS: 1 IF: verage REF: 1acdb6d df-9c7d f0d2ea OJ: pplying the Perpendicular isector Theorem and Its onverse ST: NY.NYLES.MTH.05.GEO.G.G.49.a LO: MTH MTH KEY: perpendicular bisector OK: OK 2
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