Chapter Two Review Sheet and Answers.pdf

Name:_____________________________________________________ Date:_________________ Period:_________ Geometry Chapter Two Review Sheet 1) Given triangle 𝐷𝐸𝐹 below, name the 47° angle three different ways:...

Name:_____________________________________________________ Date:_________________ Period:_________ Geometry Chapter Two Review Sheet 1) Given triangle 𝐷𝐸𝐹 below, name the 47° angle three different ways: (a) _______________ (b) _______________ (c) _______________ 2) Given the triangle below, name the following: (a) Smallest angle: _______________ (b) Largest angle: _______________ 3) Given the triangle below, name the following: (a) Smallest side: _______________ (b) Largest side: _______________ 4) In ΔABC, BD is an altitude drawn to side AC. Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ 5) In triangle 𝑃𝑄𝑅, 𝑄𝑆 is a median. If 𝑃𝑅 = 16, answer the following: (a) 𝑃𝑆 = ________ (b) 𝑅𝑆 = ________ Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ 6) In ∆ABC, BD is a perpendicular bisector. Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ 7) ⃗⃗⃗⃗⃗ 𝐴𝐵 bisects < 𝐶𝐴𝑇. If < 𝐶𝐴𝐵 = 22°, answer the following: (a) < 𝑇𝐴𝐵 = ________ (b) < 𝐶𝐴𝑇 = ________ Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ 8) Point K is the midpoint of segment TJ. (Draw a picture to the side) Statement: ____________________________ Reason: __________________________________________________________________ __________________________________________________________________ 9) Determine whether the angles are vertical angles, a linear pair, or neither. (a) < 5 and < 6 ____________________________ (b) < 5 and < 9 ____________________________ (c) < 5 and < 8 ____________________________ (d) < 6 and < 9 ____________________________ (e) < 8 and < 9 ____________________________ (f) < 5 and < 7 ____________________________ 10) Use the figure to the right to decide whether the statement is true or false. (a) If 𝑚 < 1 = 40°, then 𝑚 < 2 = 140° __________________ (b) If 𝑚 < 4 = 130°, then 𝑚 < 2 = 50° __________________ (c) < 1 and < 4 are a linear pair. __________________ (d) < 1 + < 4 = < 3 + < 2 __________________ (e) < 1 and < 4 are vertical angles. __________________ 11) Find the measure of all of the missing angles. 12) Find the value of 𝑥 and 𝑦. 13) Find the value of 𝑥. 14) Find the value of 𝑥 and 𝑦. 15) Find the measures of each labeled angle. Give a reason for your solution. 16) Two angles are supplementary. One angle is 30˚ more than another angle. Find both angles. 17) In the diagram below ⃡⃗⃗⃗⃗⃗⃗⃗⃗ 𝐴𝐵𝐶 forms a straight angle. Using the diagram, find the 𝑚 < 𝐷𝐵𝐶. Round x to the nearest tenth. (Not drawn to scale.) 18) The measures of two supplementary angles are in the ratio 2:8. What is the measure of the larger angle? 19) In the diagram below, ̅̅̅̅ 𝐴𝐵 ∥ ⃗⃗⃗⃗⃗⃗⃗⃗ 𝐷𝐸𝐹 , ̅̅̅̅ 𝐴𝐸 and ̅̅̅̅ 𝐵𝐷 intersect at 𝐶, 𝑚 < 𝐵 = 43°, and 𝑚 < 𝐶𝐸𝐹 = 152°. Which statement is true? (1) 𝑚 < 𝐷 = 28° (2) 𝑚 < 𝐴 = 43° (3) 𝑚 < 𝐴𝐶𝐷 = 71° (4) 𝑚 < 𝐵𝐶𝐸 = 109° 20) Find the following angles for each question: 21) In the diagram below of parallelogram 𝑅𝑂𝐶𝐾, 𝑚 < 𝐶 = 70° and 𝑚 < 𝑅𝑂𝑆 = 65°. What is 𝑚 < 𝐾𝑆𝑂? (Hint: Remember that we learned in this chapter that opposite sides of a parallelogram are parallel and that opposite angles are congruent.) 22) In the diagram below 𝑚||𝑛. Using the diagram, find the 𝑚 < 𝐴. 23) Find 𝑚 < 𝑛. 24) Find the value of 𝑥. 25) In 𝛥𝐴𝐵𝐶, 𝑚 < 𝐴 = 𝑥, 𝑚 < 𝐵 = 2𝑥 + 2, and 𝑚 < 𝐶 = 3𝑥 + 4. What is the value of 𝑥? 26) In the diagram below, 𝛥𝐴𝐵𝐶 is shown with 𝐴𝐶 extended through point 𝐷. If 𝑚 < 𝐵𝐶𝐷 = 6𝑥 + 2, 𝑚 < 𝐵𝐴𝐶 = 3𝑥 + 15, and 𝑚 < 𝐴𝐵𝐶 = 2𝑥 – 1, what is the value of 𝑥? 10 1 (1) 12 (2) 14 (3) 16 (4) 18 11 9 27) Which set of numbers represents the lengths of the sides of a triangle? (1) {5,18,13} (2) {6,17,22} (3) {16,24,7} (4) {26,8,15} 28) As shown in the diagram below, ̅̅̅̅ 𝐴𝑆 is a diagonal of trapezoid 𝑆𝑇𝐴𝑅, ̅̅̅̅ 𝑅𝐴 ∥ ̅̅ 𝑆𝑇̅̅, 𝑚 < 𝐴𝑇𝑆 = 48, 𝑚 < 𝑅𝑆𝐴 = 47, and 𝑚 < 𝐴𝑅𝑆 = 68. Determine and state the longest side of ∆𝑆𝐴𝑇. Explain your reasoning. ̅̅̅̅ and 𝐷𝐵 29) As shown in the diagram of ∆𝐴𝐶𝐷, 𝐵 is a point on 𝐴𝐶 ̅̅̅̅ is drawn. If 𝑚 < 𝐴 = 66, 𝑚 < 𝐶𝐷𝐵 = 18, and 𝑚 < 𝐶 = 24, what is the longest side of ∆𝐴𝐵𝐷? 30) Find the value of x in the diagram below. Name:_____________________________________________________ Date:_________________ Period:_________ Hey Geometry Chapter Two Review Sheet 1) Given triangle 𝐷𝐸𝐹 below, name the 47° angle three different ways: (a) _______________ FIFE (b) _______________ (c) _______________ EFD 2) Given the triangle below, name the following: (a) Smallest angle: _______________ 8 (b) Largest angle: _______________ c 3) Given the triangle below, name the following: (a) Smallest side: _______________ (b) Largest side: _______________ n 4) In ΔABC, BD is an altitude drawn to side AC. BDA IS BDC Statement: ____________________________ Altitudesform congruent right Reason: __________________________________________________________________ angles m __________________________________________________________________ 5) In triangle 𝑃𝑄𝑅, 𝑄𝑆 is a median. If 𝑃𝑅 = 16, answer the following: 8 (a) 𝑃𝑆 = ________ 8 (b) 𝑅𝑆 = ________ 1 8 PSERS Statement: ____________________________ Amedian divides a segmentinto Reason: __________________________________________________________________ stfu two __________________________________________________________________ congruent segments 6) In ∆ABC, BD is a perpendicular bisector. K BDA EX BDC Statement: ____________________________ Reason: Perpendicular lines formcongruent __________________________________________________________________ __________________________________________________________________ right angles AD E CD Statement: ____________________________ I M 1 A bisectordivides a segment into Reason: __________________________________________________________________ two congruentsegments __________________________________________________________________ 7) ⃗⃗⃗⃗⃗ 𝐴𝐵 bisects < 𝐶𝐴𝑇. If < 𝐶𝐴𝐵 = 22°, answer the following: 220 (a) < 𝑇𝐴𝐵 = ________ (b) < 𝐶𝐴𝑇 = ________ 440 2 227 440 CABE 4 TAB Statement: ____________________________ 25344 Anangle bisectordivides an into Reason: __________________________________________________________________ angle two __________________________________________________________________ congruent angles 8) Point K is the midpoint of segment TJ. (Draw a picture to the side) 1 E E TK E JK Statement: ____________________________ A midpoint divides a segment into Reason: __________________________________________________________________ two __________________________________________________________________ congruentsegments 9) Determine whether the angles are vertical angles, a linear pair, or neither. Neither (a) < 5 and < 6 ____________________________ Linear Pair (b) < 5 and < 9 ____________________________ VerticalAngles (c) < 5 and < 8 ____________________________ Neither (d) < 6 and < 9 ____________________________ Linear Pair (e) < 8 and < 9 ____________________________ Neither (f) < 5 and < 7 ____________________________ 10) Use the figure to the right to decide whether the statement is true or false. (a) If 𝑚 < 1 = 40°, then 𝑚 < 2 = 140° False __________________ True (b) If 𝑚 < 4 = 130°, then 𝑚 < 2 = 50° __________________ (c) < 1 and < 4 are a linear pair. True __________________ (d) < 1 + < 4 = < 3 + < 2 True __________________ (e) < 1 and < 4 are vertical angles. False __________________ 11) Find the measure of all of the missing angles. 12) Find the value of 𝑥 and 𝑦. 300 106 180 44 150 1060 1500 300 n so 5 7 2920 180 14191343ft 42 440 7 9020 180 12 2420180 y 2920180 121107 110410 7 70 1202920180 7 7 2944818 XD 24 49 lied 13) Find the value of 𝑥. 14) Find the value of 𝑥 and 𝑦. 2 14 90 34 90 7 3 3 307 4 Ex 2 3 90 180 4 2 4 180 41807 2 180 30 188 188 9 60 2 4 180 915 83011 9228 88 9 188 Ix8D 1227 19 15) Find the measures of each labeled angle. Give a reason for your solution. 1400 400 180145 3 180 481400 3602 22 2380 350 Supplementary angles Supplementary angles 48 vertical angles are congruent 1400 Vertical anglesarecongruent vertical totb 2380 Adjacentanglesaround a point 16) Two angles are supplementary. One angle is 30˚ more than another angle. Find both angles. 80 Fbi30 X 1 30 180 2 1338 1838 42 42 7530 21 150 1422 1050 2 2 4 75 17) In the diagram below ⃡⃗⃗⃗⃗⃗⃗⃗⃗ 𝐴𝐵𝐶 forms a straight angle. Using the diagram, find the 𝑚 < 𝐷𝐵𝐶. Round x to the nearest tenth. (Not drawn to scale.) 5 2 207 5 180 KDBC 2 20 5 8 25 180 4DBC 3 25 25 8 155 8 25 TT DBC 349.4725 KDBE83 A 8 4 19.375 119.47 18) The measures of two supplementary angles are in the ratio 2:8. What is the measure of the larger angle? 8x 2 84 180 8118 104 180 01440 10 10 4 18 3 19) In the diagram below, ̅̅̅̅ 𝐴𝐵 ∥ ⃗⃗⃗⃗⃗⃗⃗⃗ 𝐷𝐸𝐹 , ̅̅̅̅ 𝐴𝐸 and ̅̅̅̅ 𝐵𝐷 intersect at 𝐶, 𝑚 < 𝐵 = 43°, and 𝑚 < 𝐶𝐸𝐹 = 152°. alternate 28 43 180 180 2 interiors Ig 7 0 Yo 43 78 Which statement is true? 180152280 (1) 𝑚 < 𝐷 = 28° (2) 𝑚 < 𝐴 = 43° (3) 𝑚 < 𝐴𝐶𝐷 = 71° (4) 𝑚 < 𝐵𝐶𝐸 = 109° O 20) Find the following angles for each question: BS Bs SB Is SB s 480 1320 48 480 Corresponding 18048 1320 Anttegrtengies Alternate A s ftp.osigneges Exterior Angles 21) In the diagram below of parallelogram 𝑅𝑂𝐶𝐾, 𝑚 < 𝐶 = 70° and 𝑚 < 𝑅𝑂𝑆 = 65°. What is 𝑚 < 𝐾𝑆𝑂? (Hint: Remember that we learned in this chapter that opposite sides of a parallelogram are parallel and that opposite angles are congruent.) 70 180 180 7 65 135 45 1350450 1350 4513A Foo y IS ina parallelogram 22) In the diagram below 𝑚||𝑛. Using the diagram, find the 𝑚 < 𝐴. Bs 2 10 8614 2 10 180 S B 21767 10 162 10 86 1620 180 BS 10 10 S B x 76 18021 144  23) Find 𝑚 < 𝑛. 24) Find the value of 𝑥. ternate 35 terior4 syst 35 37 37 72 4 188 189 35 810 990 810 370 810I Kn 13707 25) In 𝛥𝐴𝐵𝐶, 𝑚 < 𝐴 = 𝑥, 𝑚 < 𝐵 = 2𝑥 + 2, and 𝑚 < 𝐶 = 3𝑥 + 4. What is the value of 𝑥? 2 2 3 4 180 6 166 1806 611 174 6 6 12907 I ExteriorAngleTheorem 26) In the diagram below, 𝛥𝐴𝐵𝐶 is shown with 𝐴𝐶 extended through point 𝐷. Exteriors sum of the 6 2 3 15 2 1 nonadjacentinteriors's 6 2 5 14 SX SX 3 15 6 2 4 2 14 2 2 IED If 𝑚 < 𝐵𝐶𝐷 = 6𝑥 + 2, 𝑚 < 𝐵𝐴𝐶 = 3𝑥 + 15, and 𝑚 < 𝐴𝐵𝐶 = 2𝑥 – 1, what is the value of 𝑥? 10 1 (1) 12 (2) 14 (3) 16 (4) 18 O 11 9 2 27) Which set of numbers represents the lengths of the sides of a triangle? (1) {5,18,13} (2) {6,17,22} (3) {16,24,7} (4) {26,8,15} O 1677724 6125333 815726 838 23,24 23426 28) As shown in the diagram below, ̅̅̅̅ 𝐴𝑆 is a diagonal of trapezoid 𝑆𝑇𝐴𝑅, ̅̅̅̅ 𝑅𝐴 ∥ ̅̅ 𝑆𝑇̅̅, 𝑚 < 𝐴𝑇𝑆 = 48, 𝑚 < 𝑅𝑆𝐴 = 47, and 𝑚 < 𝐴𝑅𝑆 = 68. 68 180 6567 47 115 48 113 1150650 Y alternateinteriors Determine and state the longest side of ∆𝑆𝐴𝑇. Explain your reasoning. The longest side of triangle SAT is ST. It is the longest side because it is opposite the largest angle. ̅̅̅̅ and 𝐷𝐵 29) As shown in the diagram of ∆𝐴𝐶𝐷, 𝐵 is a point on 𝐴𝐶 ̅̅̅̅ is drawn. If 𝑚 < 𝐴 = 66, 𝑚 < 𝐶𝐷𝐵 = 18, and 𝑚 < 𝐶 = 24, what is the longest side of ∆𝐴𝐵𝐷? 18 180 180 42 1808 24 42 138 1080 720 420 1380 420 421387 The longest side of triangle ABD is AB. 30) Find the value of x in the diagram below. ExteriorAngleTheorem 110 2 30 60 Exteriors sum of the nonadjacentinteriors's 110 2 90 90 90 20 24 2 2 HOD