opic 4 ongruent riangles PP Name: Period: eacher: 1 P a g e
2 nd Six Weeks 2015-2016 MONY USY WNSY HUSY FIY Oct 5 6 7 8 9 3.4/3.5 Slopes, writing and graphing equations of a line HW: 3.4/3.5 Slopes, writing and graphing equations of a line etest #3 in teacher s room HW: eview eview est #4 12 13 14 15 16 4.2 riangle congruence 4.1/4.7 riangle sum properties and Isosceles 4.1/4.7 riangle sum properties and Isosceles 4.1/4.7 riangle sum properties and Isosceles 4.3-4.6 riangle Proofs #1 Proofs HW: riangles HW: riangles HW: riangles HW: HW: 19 20 21 22 23 4.3-4.6 riangle Proofs #3 Proofs 4.3-4.6 riangle Proofs #4 Proofs eview eview est #5 HW: Have first 20 proofs completed HW: Have first 30 proofs done 26 27 28 29 30 5.1 midsegment theorem and coordinate proofs 5.5 Use inequalities in a triangle 5.2/5.3/5.4 ltitude, median, angles bisector and perpendicular 5.2/5.3/5.4 ltitude, median, angles bisector and perpendicular 5.2/5.3/5.4 ltitude, median, angles bisector and perpendicular bisector bisector bisector etest #5 in Minitheater HW: Nov 2 3 4 5 6 5.6 Hinge heorem Practice with Writing equations of altitudes, median, perpendicular bisectors HW: eview Scavenger Hunt eview Scavenger Hunt est #6 2 P a g e
Worksheet #1 fter est #4 PP hapter 4 lassify each triangle by sides. 1. 8 2. 3. 11 4. 10 6 4 8 8 12 11 7 6 4 lassify each triangle by angles. 5. 6. 7. 8. 115 30 57 60 30 78 45 35 60 60 60 lassify each triangle. (raw a picture to help) 9. with. 10. F with m 90. 11. JKL with JK KL LJ. 12. MNP with MN NP PM. 13. QS withm Q 145, m 15, and m S 20. 14. ngle Measures he measure of one interior angle of a triangle is 32. he other interior angles are congruent. Find their measures. 15. In, m 42. he measure of is five times the measure of. Find m and m. Write and solve an equation to find each of the following. 16. S 17. 3x 4 2x 6 5x U 40 V W 6x 4 3 P a g e
= UW = I 54 5x 9 18. 19. 2x (3x 6) G GH = 7x H X ( x 6) Z m Z = m = 20. 88 21. perimeter = 84 2x 3n 8 3x 4 9n = 2n 4 = m = In xercises 22 24, use the following information. lassroom he desk layout for a classroom is shown in the coordinate system measured in feet. Use istance formula (Pythagorean theorem) 22. Find the shortest distance in inches from to, to, and to, if you can walk between desks. 23. Find the shortest distance in inches from to, to, and to, if you can walk between desks. 24. Find the shortest distance in inches from to, to, and to, if you can not walk between the desks. 4 P a g e
Practice determining the type of triangle on a coordinate plane Graph the points, find the length of each side and classify the triangle by sides. etermine if the triangle is a right triangle using slope. (Hint: find the slope of each side and remember what make lines perpendicular. 1) ( 1,4), (5,1), ( 3,0) 2) (2, 3), ( 2, 6), ( 5, 2) 3) ( 4,1), U( 1, 2), G (2,5) 4) P( 4,1), U( 1, 4), K (3,5) 5 P a g e
Worksheet pplying ongruence in riangles I. omplete each correspondence statement. Period 1) S 2) 3) GHK F S M N II. Write a congruence statement for each pair of congruent triangles. G K H 4) 5) 6) N S F W I V O K M G III. Label the corresponding part if S. Use the figures to complete each statement. 7) 8) S 9) 10) S 11) S 12) IV. Find the value of x. 13) Given F, =15, =20, =25, and F=3x-7 14) Given F, =10, F=13, F=16, and =4x-8 15) 6 P a g e
16) 17) 17 17) 18) 19) 20) 21) 22) 7 P a g e
23) P N, 40, N 60, (210), find the value of x and m. 24) OG, O ( x y), 30, 100, (9y 19) find the value of x, y, and OG. 25) F, 2x 10, 12 2y, 6x 2, F 3y 2, 5y find the value of x, y, and. 26) OY GI, O 4x 6, OY 5x, GI x 9, I 3y find the value of x, y, and I. 8 P a g e
Worksheet #2 hapter 4 Find the value of x. Show all work to receive credit Period 1) x = 2) x = 3) x = 58 (3x-1) 47 96 21 31 4) x = 5) x = 6) x = 100 94 21 34 (2x+3) 51 60 2 7) x = 8) x = 9) x = 10 23 (x+40) (3x-17) (2x-5) 10) x = 11) x = 12) x = 43 65 50 44 57 80 13) x = 14) x = 15) x = 122 (6x-7) (103-x) 2 9 P a g e
16) x = 17) x = 56 50 53 62 80 Find the measure of each angle. 18) 1 19) 2 20) 3 3 4 90 21) 4 22) 5 23) 6 6 5 2 1 68 Find the measure of the numbered angle. 24) m 1 25) m 2 26) m 3 27) m 4 28) m 5 29) m 6 Find the value of x and y. 30) 31) 32) 10 P a g e
Isosceles riangle Properties I. Find the missing value. 1) x = 2) x = 3) x = 3x-6 (4x-20) 3 x+10 28 4) x = 5) x = 6) x = 5 2 4x+2 60 6x-30 (3x+10) (5x-10) 7) x = 8) x = 9) x = 116 63 10) x = 11) x = 12) x = (4x+10) 54 (4x+20) 40 40 13) x = 14) x = 15) x = 9x-5 4x+20 100 (17x-28) 3 16) x = 17) x = 18) x = 4x+12 5 121 60 2x+32 11 P a g e
19) x = 20) x = 21) x = 4 (6x-20) 2 31 112 22) x = 23) x = y = 24) P = 143 121 y Q 6x-12 3x+12 P 9x+2 25) x = y = 26) w = x = y = z = 22 37 65 y w z y 27) x = y = 28) x = y = 29) x = y = z = z = z = Find the perimeter of the triangle. 30) 31) 32) 12 P a g e
riangle Proofs hapter 4 omplete a flow proof for each. 1) Given:, F, and are right angles. Prove: F F 2) Given:, is the midpoint of. Prove: 3) Given: is the midpoint of, bisects,. Prove: 4) Given: G F, is the midpoint of GF, G GF, F GF. Prove: G F G F 5) Given:,. is the midpoint of, Prove: 13 P a g e
6) Given:, Prove: 7) Given: bisects, bisects. Prove: 8) Given:,. Prove: 9) Given: bisects F, F bisects, F. Prove: F F 10) Given: S bisects S,. Prove: S S S 14 P a g e
11) Given: bisects Prove:, bisects. 12) Given: WJ KZ, W and K are right angles Prove: JWZ ZKJ W J Z K 13) Given: JL LM, LJ JK, MJ KL Prove: JLM LJK M L J K 14) Given:, bisects. Prove: 15) Given:, and is the midpoint of. Prove: are right angles, 15 P a g e
M 16) Given: LO bisects MLN, OM LM ON LN Prove: LMO LNO L O N 17) Given: 1 2, 3 4, is the midpoint of. Prove: 1 3 4 2 18) Given:,. Prove: Q 19) Given: PQ QS, S SQ, is the midpoint of QS Prove: PQ S P S G 20) Given: HV G, GH V, G bisects HV Prove: IGH IV H I V 16 P a g e
21) Given:,. Prove: 22) Given:,. Prove: 23) Given: 1 2, 3 4. Prove: 4 2 1 3 24) Given:,. Prove: bisects 25) Given: Q bisects Prove: Q bisects S S,Q S. Q S 17 P a g e
26) Given: L J, KJ LM Prove: LKM JMK K J L M K 27) Given: JK PQ, KJ QP Prove: KQ bisects JP M P J Q 28) Given:, Prove: 28) Given: bisects, is the midpoint of Prove: 18 P a g e
29) Given:, Prove: 30) Given: 1 2, 3 4 Prove: Q QU Q 3 4 1 2 U 31) Given: Q U, Q U Prove: Q U Q U 32) Given:, Prove: F 19 P a g e
hapter 4 eview PP Name Identify each triangle by its angles. 1. 2. 3. 4. 125 50 60 Identify each triangle by its sides. 5. 6. 5 5 7. 8. Identify the following triangles by angles and sides: 9. 10. 70 11. 12. Solve for x. 13. x = 14. x = 5x 4x + 7 115 x 4x + 7 3x + 13 6x - 7 15. x = 16. x = 3x + 20 6x + 12 70 32 17. x = 2x 3x + 10 18. x = 20 P a g e 2x 42 4x - 16
Write a congruence statement for 19-22: H Q 19. 20. S L N F I 21. M 22. Q H P N raw a set of triangles, label them, and answer the questions for 23-25. 23) MY JF, if M 5, F 7, and Y 3, then find J, JF, and the perimeter of JF. 24) O, if m 30 and m 80, then find m,m, m O,and m. 25) P WOK, If 21, P 35, and WO 7x 7, find the value of x and WO. F etermine if the triangles are congruent, if congruent give postulate or theorem for why the triangles are congruent. If not congruent write no. J G I 40) F 41) JHG JHI J 42) NKL LMN F N M G H I K L 43) OPS QP 44) WV UV 45) XZ ZYX O Q U X P Y S W V Z 46) GF 47) HJI LMK 48) PON SQ G J K N S H L F I M O P Q 49) 21 P a g e
50) Given: F U Prove: is the midpoint of UG FU G F G 51) Given: P IQ P P bisects IPQ Prove: IP QP I Q U 52) Given: V UV W is the midpoint of V Prove: 1 2 1 2 W V 53) 54) 22 P a g e