Page 1 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 1, Mathematics 8, Third Quarter, Learning Objective: illustrate the need for axiomatic structure of a mathematical system, in general and in Geometry in particular the Defined terms., I. Name all the segments, rays and opposite rays in the figure below., Line Segments, , Rays, , Opposite Rays, , II. A. Identify each figure that contains points X and Y as a line segment, a line, or a ray., , B. Use a ruler or straightedge to draw each figure., , III. Complete the following statement. Write sometimes, always, or never., , 1. If C is the midpoint of XY, then C is ______________ between X and Y., 2. Four points ______________ lie in one plane., 3. �� and �� are ______________the same line., 4. �� and �� are ______________the same rays., 5. Three distinct points will ______________lie on the same line., 6. A ray has______________ a midpoint., 7. Two points ______________lie in exactly one line., 8. If point S is between R and V, then S ______________ lies on Line RV., 9. The length of a segment is ______________ negative., 10. If A, B, and C are coplanar and B is equidistant from points A and C, then B, is______________ the midpoint of AC., IV. Solve the following:, A. C is between A and E. For each problem, draw a picture representing the three points, and the information given and solve for the indicated:, 1. If AC = 24 in. and CE = 13 in., AE = _____., 2. If CE = 7in. and AE = 23 in., AC = _____., B. Refer to the figure and the given information to find each measure., 3. Given : AC = 39 m, 4. Given the figure and DG = 60 ft., , 5. B is the midpoint of AC., , Prepared by: Flora S. Isada MT2, LPENHS Main, , 1

Page 2 : Learning Activity Worksheets 1- Week 1- Day 3&4 : Undefined Terms, Learning Objective: identify and describe the three (3) Undefined Terms: Point; Line; and, Plane.and associate in real life situations., , I., , _____, _____, _____, _____, _____, , Direction: Determine the undefined term suggested by each of the, following. if the object represents a POINT, PLANE or LINE. Write your P if, point, L if line and PL if plane on the space provided., 1., 2., 3., 4., 5., , II., , Spaghetti noodles, Chess board, Tip of a needle, Railway, Ceiling of a room, , _____ 6. Stars seen in the sky, _____ 7. A mole on your face, _____ 8. A kite’s string, _____ 9. Hair strand, _____ 10. Swimming pool, , Direction: Determine if the three points listed below are Collinear or, Noncollinear and if so, name which line they lie either ���� � ��� ���� �., Refer your answer on figure 1, figure 1, , 1. �, �, � _________________________ 5. �, �, � ____________________, 2. �, �, � ________________________ 6. �, �, � ______________________, III., , 7. �, �, � _____________________, 8. �, �, � ____________________, , Direction: Name the point that is coplanar with the given points. Refer your, answer on figure 2., ___________, 1. �, �, ��� �, 2. �, �, ��� �, ___________, ___________, 3. �, �, ��� �, 4. �, �, ��� �, ___________, ___________, 5. �, �, ��� �, figure 2, Applying Skills, IV., 1. Miss Claire Santos observes a mark of a nail in the ceiling. The mark of the nail, represents ____________., 2. Stephany observes a mark of a nail in the ceiling. The ceiling represents _________., 3. Robert observes a rod lying on the ceiling. The rod represents ________________, , Prepared by: Florence C. Soriano T1, LPENHS -EVA, , 2

Page 3 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets #1, Mathematics 8, Third Quarter, Week 2- Day 1&2: Postulates, Learning competency: to illustrate the need for an axiomatic structure of a, , mathematical system in general, and in Geometry in particular postulates., , Directions: Using the given figures, determine the postulate that justifies the following, statements., A, B, , -6, , F, , -3, , C, 1, , E 0, , K, 0, M, 0, I, 0, N, 0, 1., 2., 3., 4., 5., 6., 7., 8., 9., , G0, , 0, , �∠��� = �∠��� + �∠���, �� = −7, , �∠��� = �∠��� + �∠���, , ∠��� and ∠��� are supplementary., �� = −4, , �∠��� = �∠��� + �∠���, �� = −3, , ∠��� and ∠��� are supplementary., �∠��� + �∠��� = �∠���, , 10. �� = 4, , 3, , H0

Page 4 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets #1, Mathematics 8, Third Quarter, Week 2 Day 3&4 : Theorems, Learning competency: to illustrate the need for an axiomatic structure of a, , mathematical system in general, and in Geometry in particular theorems., , Directions: Complete the following statements using the given figures below., G, , I, , 2, 1 4, 3, H, O, , M, , P, N, , Q, , 1., 2., 3., 4., 5., 6., 7., 8., 9., , ∠1 ≅ __________, , If ∠� ≅ ∠�, then __________., , If ∠��� and ∠��� are right angles, then __________., ∠��� ≅ __________, , If �� ≅ ��, then __________., If ∠� ≅ ∠�, then __________., ∠2 ≅ __________, , If ∠��� and ∠��� are right angles, then __________., ∠��� ≅ __________, , 10. If �� ≅ ��, then __________., , 4

Page 5 : Learning Activity Worksheets # 1, Mathematics 8, Third Quarter, Week 3 Day 1&2: TRIANGLE CONGRUENCE, Learning Competency: Illustrates triangle congruence., A. Directions: Complete each statement to make it true., 1. If ∆BIO ≅ ∆SCI, then, , a. BI ≅ _______, , b. BO ≅ _______, , c. IO ≅ _______, , e. ∠I ≅ _______, , d. ∠O ≅ _______, , f. ∠B ≅ _______, , B. Directions: Write the corresponding congruence between each pair of, triangles., , 1. Given: ∆��� ≅ ∆���, , 2. Given: ∆��� ≅ ∆���, , C. Directions: Complete each congruence statement by naming the, corresponding angle or side., 1. ∆��� ≅ ∆���, , DE ≅, , 2. ∆��� ≅ ∆���, , ?, , ∠V ≅, , 3. ∆��� ≅ ∆���, , UV ≅, , ?, , 4. ∆��� ≅ ∆���, , ?, , ∠YXZ ≅, , 5. ∆��� ≅ ∆���, , DE ≅, , 5, , ?, , ?

Page 6 : Third Quarter, Week 3 –Day3&4: Illustrate the SAS Congruence Postulate (Side-Included, Angle Side), Learning competency: To illustrate the SAS Congruence Postulate (Side-Included, Angle-Side), I. Fill in the blank., If the two sides and the (1) __________________ of one triangle is congruent to the, (2) _____________ and the included angle of another triangle, then the two triangles are said, to be congruent. The (3) _______________ is the angle made at the point where two sides of a, triangle meet. The two triangles shown below are (4) ___________ by, (5) ____________ postulate., , II. What will be the value of p, q and r if ∆ABC ≅ ∆DEF?, , p = __________, , q = _____________, , r = ____________, , III., , 6

Page 8 : Lydia Aguilar National High School, NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 2, Mathematics 8, Third Quarter, Week 4 - Day 3&4: SSS Congruence Postulate, Learning Objective: Illustrate SSS Congruence Postulate and prove the congruence, of triangles using SSS Postulate, I. Write the proper congruence statement for the following triangles, , II. Fill in the blanks., E, , P, , R, , N, , A, , M, , 1. ��  _____, 2. ��  _____, 3. ___ ��, , 4. ___  ��, , 5. PEN   ____, III. Given : �� ≅ �� , �� ≅ ��, Prove : ABC ≅ ADC, , Statements, , Reasons, , 1. �� ≅ ��, , 1. _______________, , 2. ________________, , 2. Given, , 3. ________________, , 3. Reflexive Property, , 4. ABC ≅ ADC, , 4. ________________, , 8

Page 9 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 2, Mathematics 8, Third Quarter, Week 5 – Day 1 & 2 Corresponding Parts of Congruent Triangles are Congruent, Learning competency:, Solves corresponding parts of congruent triangles, Direction: Complete the angle measurements of the congruent triangles below., Solution:, Solution:, 1) BAC  EDF, Solve for x., Solve for mB., , 2) BAC  EDF, , Solution:, Solve for y., , Solution:, Solve for mU., , 3) GHI  JKL, , Solution:, Solve for y., , Solution:, Solve for x., , 4) JKL  PQR, mK = (90 – y), mQ = 13, , Solution:, Solve for y., , Solution:, Solve for mK., , 5) ABC  XYZ, mA = (5x – 10), mX = 35, , Solution:, Solve for x., , Solution:, Solve for mA., , 9

Page 10 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets #2, Mathematics 8, Third Quarter, Worksheet 5 Week 5 – Day 3 & 4 : Corresponding Parts of Congruent Triangles are, Congruent, Learning competency:, Solves corresponding parts of congruent triangles, Direction: Complete the angle measurements of the congruent triangles below., Solution:, Solution:, 1) QSP  QSR, Solve for y., If QS = 24, then solve, for QP., , 2) STU  VWX, , Solution:, Solve for x., , Solution:, Solve for ST., , 3) ABC  DEF, , Solution:, Solve for x., , Solution:, Solve for y., , 4) JKL  PQR, JK = 5x - 31, KL = -3y – 1, PQ = x + 1, QR = 9 – y, , Solution:, Solve for x., , Solution:, Solve for y., , 5) ABC  XYZ, AB = 2x + 1, BC = 2y + 11, XY = x + 7, YZ = 4y + 3, , Solution:, Solve for x., , Solution:, Solve for y., , 10

Page 11 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets #3, Mathematics 8, Third Quarter, Week 6 – Day 1 – 4 : Proves two triangles are congruent, Learning competency: to proves two triangles are congruent, 1. Given: AB  EL , BG  IE and AI  LG, Prove: ABG  LEI, Proof:, Statements, , 1., 2., 3., 4., 5., 6., 7., 8., , AI  LG, IG  IG, , AI  IG  LG  IG, AI  IG  AG, LG  IG  IL, AG  IL, AG  IL, AB  EL , BG  IE, ABG  LEI, , Reasons, , 1. Given, 2. Reflexive Property, 3., 4., 5., 6., 7. Given, 8., , 2. Given: 1  2 , PR  RO , TM  MO and, , O is the midpoint of RM, Prove: PRO  TMO, Proof:, 1., 2., 3., 4., 5., 6., 7., , Statements, , 1  2, O is the midpoint of RM, , PR  RO , TM  MO,  R and M are right angles, R  M, PRO  TMO, , Reasons, , 1., 2., 3. Definition of midpoint, 4., 5., 6., 7., , 11

Page 12 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 3, Mathematics 8, Third Quarter, Week 7 – Day 1 & 2 : Proves statements on Triangle Congruence., Learning competency: to proves two triangles are congruent, Set A: Give the congruence required to prove right ∆MEG ≌ right ∆SON., E, , M, 1., 2., 3., 4., 5., , O, , G, , S, , Given, MG ≌ SN; ∠G ≌ ∠N, EG ≌ ON; ∠G ≌ ∠N, EM ≌ OS; ∠M ≌ ∠S, MG ≌ SN; ME ≌ SO, EG ≌ ON; ME ≌ SO, , N, , Right Triangle Congruence Theorem, , Set B: Complete the proof., , HA Congruence Theorem, *If the hypotenuse and an acute angle of a right triangle are congruent to the, corresponding hypotenuse and an acute angle of another right triangle, then the, two right triangles are congruent., , Given: ∠P and ∠I are right angles., OQ ≅ KJ, ∠Q ≅ ∠J., Prove: ∆OPQ ≅ ∆KIJ, Proof:, Statements, 1. OQ ≅ KJ, ∠Q ≅ ∠J, 2., (1), 3., (2), 4.∆OPQ ≅ ∆KIJ, , 1.Given, 2.Given, 3., 4., , Reasons, (3), (4), , To complete the proof, find the missing statement or reason below. Choose the letter of the, correct answer., A. ∠Q ≅ ∠J, C. ∠P and ∠I are right angles., B. Right Angle Postulate, D. AAS Congruence Theorem, 12

Page 13 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 3, Mathematics 8, Third Quarter, Week 7 – Day 3 & 4 : Proves statements on Triangle Congruence., Learning competency: to proves two triangles are congruent, Set A: CROSSWORD PUZZLE, Directions: Solve the puzzle by using the hint given across and down, , Set B: Complete the proof., . Converse of Isosceles Triangle Theorem:, *If two angles of a triangle are congruent, then the sides opposite those angles are, congruent., Given: ∆ABC and ∠A ≅ ∠B, Prove: AC ≅ BC, Proof:, Statements, Reasons, 1., 1. Draw CH, the bisector of ∠ACB, intersecting AB at H., 2., 2. ∠ACH ≅ ∠BCH, 3., 3. ∠A ≅ ∠B, 4., 4. CH ≅ CH, 5., 5. ∆AHC ≅ ∆BHC, 6., 6. AC ≅ BC, Choose the reasons below. Write them in the appropriate column to complete the proof., ●CPCTC, ●Reflexive Property, ●Angle Bisector Theorem, ●SAA Theorem, ●Given, ●Definition of Angle Bisector, , 13

Page 14 : NAME: ___________________________________________, , Score: ___________________, , GRADE & SECTION ______________________________, , Teacher: _________________, , Learning Activity Worksheets # 4, Mathematics 8, Third Quarter, Week 8 – Day 1-4 Applying Triangle Congruence to Construct Perpendicular Bisector, Learning competency: Applies the Perpendicular Bisector Theorem to find the measure of the, parts of congruent triangles., , �� is a perpendicular bisector of ∆DAB and ∆ABE, �� = 10,, , �� = 17, ∠ADC = 42° and ∠BEC= 33°, find the measure of the, following segments and angles., 1. ∠BDC, 2. ∠AEC, 3. ∠DAC, 4. ∠DBC, 5. ∠EAC, 6. ∠EBC, 7. ∠BCD, 8. ∠BCE, 9. ��, 10. ��, , A. Find the value of x., , 14

Page 15 : Learning Activity Worksheets # 4, Mathematics 8, Third Quarter, Week 9 – Day 1-4 Apply triangle congruence in constructing perpendicular and angle, bisector., Learning competency: Apply triangle congruence in constructing perpendicular and angle, bisector., , A. Complete the given proof by placing the correct statement and reason on each of the box., Choose your answers from the pool of choices below. Reasons may be chosen more than once., <DAE ≅ <DRE, ED bisects <REA, , STATEMENTS, <AED ≅ <RED, DR ┴ ER, DA ┴ EA, ED ≅ ED, AD ≅ RD, , Definition of, perpendicular lines, Given, , REASONS, HyA Congruence, Definition of angle, Theorem, bisectior, Reflexive Property, All right angles are, congruent, , Given: ED bisects <REA, DR ┴ ER, DA ┴ EA, D is a point on ED, Prove: AD ≅ RD, 1., 2., 3., 4., 5., 6., 7., 8., , Statements, , ∆ADE ≅ ∆RDE, <DAE and <DRE are, right angles, , Reasons, , B. Given that BC = DC and AB ┴ CB, AD ┴ CD., Find the following given their measurements, 1. m<BAC = (4x + 18)°; m<DAC = (2x + 30)°, a. x, b. m<BAC, c. m<DAC, 2. BC = 7x – 8; DC = 4x + 4, a. x, b. BC, c. DC, 3. m<BAC = (6x + 5)°; m<DAC = (2x + 45) °, a. x, b. m<BAC, c. m<DAC, 4. Find m<ADC, , 15, , CPCTC

Page 16 : C. Directions: Answer the following questions:, 1. Is there enough information to determine if, AB is the bisector of <CAD? Why or why not?, , 2. A 100° angle is bisected. What are the resulting angles?, , 3. What should be the measure of x so that CB = DB?, , B. Using the steps in constructing angle bisector in a triangle, draw one example of your own., , 16