CHOOSE THE CORRECT ANSWER.

@ Pro-test Directions: Read and analyze the questions below. Write onlyr the letter of the eorreet answer. 1. which theorem states that the sum of the lengths of an}.F two sides is greater than the length of the third side? A. Exterior Angle Theorem (3. Triangle Inequality Theorem E. Hinge Theorem D. IConverse of the Hinge Theorem For numbers 2 and 3, consider an isosoeles aPRN with base W. Point T is between points P and N. 2. If mLPRT :- mLNRT, what relation exists between the lengths of W and W? A. 2- E. 4: C. - D. cannot be determined 2. If myPRT > m/NRT, what relation exists between the lengths of PT and NT? A. > C. = B. XS. Therefore, mZXTE > mzXTS. X A. Exterior Angle Inequality Theorem B. Hinge Theorem C. Triangle Inequality Theorem E T S D. Converse of the Hinge Theorem5. Mark has proved that BS > BW. Which of the following statements is not part of his proof? Figure: W E 1150 S B A. ES = EW B. EB ~ EB C. ZSEB > ZWEB D. ZW XS. Therefore, mZXTE > mZXTS. X A. Exterior Angle Inequality Theorem B. Hinge Theorem C. Triangle Inequality Theorem E T S D. Converse of the Hinge Theorem 5. Mark has proved that BS > BW. Which of the following statements is not part of his proof? Figure: W E 1150 S B A. ES ~ EW B. EB ~ EB C. ZSEB > ZWEB D. ZW LD5 D 2 6 G Figure 1 N Proof: Statements Reasons 1. AGLN, DN bisects / GNL 1. 2. 2. An angle bisector divides an angle into two congruent parts. 3. mz4 = mz1 + mz3 3. 4. m 24 > mz3 4. The whole is greater than its parts. 5. m24 > m26 5. 6. NL > LD 6.Activity 3: Just Give Me Your Reasons! Fill in the blanks with definition, property, postulate or theorem that will prove the Exterior-Angle Inequality Theorem. Given: AWPR is isosceles with base PR, R is the midpoint of PY. Prove: WY > WPW P R Y Figure 3 Proof: Statements Reasons 1. R is the midpoint of PY 1. 2. PR = RY 2. 3. AWPR is isosceles with base PR 3. 4. PW = RW 4. 5. 5. 21 > 22 6. 6. WY > WR 7. 7. WY > WPAevity 4: Prove Yourself Prove by Converse of the Hinge Theorem. R Given: LRSI} E LRDS, E 2'? 51" 8 Prove: mLDRT :- mLSRT Figure 4 & Remember 5 The following steps have to be observed in writing proofs: 1. Draw the figure described in the problem. The figure may have already been drawn for you, or you may have to draw it yourself. Label your drawn gure with the information from the given by: marking congruent or unequal angles or sides, marking perpendicular, parallel or intersecting lines or indicating measures of angles and,r or sides. The markings and the measures guide you on how to proceed with the proof. They also direct you whether your plan for proof requires you to make additional constructions in the gure. 2. Write down the reasons carefully. Some of the first reasons are often the given statements (but not always), and the last step is the statement that you set out to prove. MA.LIZA M. RECANA MATH & QUARTER 4 WEEK 3 Page 8 10 Check your Understanding Application: Jay wants to visit his friend Ken, but due to Covid-19, he can't take the shorter route. He needs instead to pass Mark's house to reach Ken's that definitely take a longer distance. Their houses are of different distances from each other and in a triangular path. Using this scenario, write a two-column proof that proves triangle inequality.Illustration: K K M M Given: AKJM, JI > ML by construction Construction: Extend /K to L where KL = KM. Prove: JK + KM > JM Join Points M and L. 21 = 42 (Sides opposite the equal angles are equal Post-test Directions: Read and analyze the questions below. Write only the letter of the correct answer. 1. Which theorem states that the sum of the lengths of any two sides is greater than the length of the third side? A. Exterior Angle Theorem C. Triangle Inequality Theorem B. Hinge Theorem D. Converse of the Hinge Theorem For numbers 2 and 3, consider an isosceles APRN with base PN. Point T is between points P and N.Activity 2: Show Your Proof Write the definition, property, postulate or theorem that will prove each of the given statements using the Hinge Theorem. Given: O is the midpoint of CV C O V mz1 = mz2, and mz3 = mz4 3 Prove: DC > IV 2 D Figure 2 Proof: Statements Reasons 1. O is the midpoint of CV 1. 2. 2. Given 3. 3. Definition of Midpoint 4. 21 = 22 4. 5. DO = 10 5. Converse of Isosceles Theorem 6. AB > ED 6