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Exercise B. Complete the Proof table to prove the theorem. Given: DL || KM Prove AD L AL AK AM Proof Statements Reasons

Exercise B. Complete the Proof table to prove the theorem. Given: DL || KM Prove AD L AL AK AM Proof Statements Reasons

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use statement 8 in 15 statement 14. Substitution Use symmetric Property 16 in statement 15. Symmetric Property of Equality Use Inversion Property in 17 statement 16. Inversion Property of Proportion TRIANGLE ANGLE-BISECTOR THEOREM APPLICATION Solve for the unknown side applying the Triangle Angle-Bisector Theorem. Note that the figures are not drawn to scale. 18 Solution: 25 Example: - 15s = 25 (18) 18 %3! 40 25 15 25(18) 15 450 18 140-25 = 15 40 25 15 s = 30 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally. Exercise B. Complete the Proof table to prove the theorem. Given: DL || KM Prove AD AL %3D AK AM Proof Statements Reasons 1. DL | KM 1.
Transcribed Image Text:Use statement 8 in 15 statement 14. Substitution Use symmetric Property 16 in statement 15. Symmetric Property of Equality Use Inversion Property in 17 statement 16. Inversion Property of Proportion TRIANGLE ANGLE-BISECTOR THEOREM APPLICATION Solve for the unknown side applying the Triangle Angle-Bisector Theorem. Note that the figures are not drawn to scale. 18 Solution: 25 Example: - 15s = 25 (18) 18 %3! 40 25 15 25(18) 15 450 18 140-25 = 15 40 25 15 s = 30 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally. Exercise B. Complete the Proof table to prove the theorem. Given: DL || KM Prove AD AL %3D AK AM Proof Statements Reasons 1. DL | KM 1.
2. Corresponding angles are 2. congruent. 3. ADAL - A KAM Similarity Theorem 3. 4. Definition of similar polygons 4. TRIANGLE PROPORTIONALITY THEOREM APPLICATION Solve for the unknown sides in the figures. The first one is done for you. Note that the figures are not drawn to scale. Solutions Solving for r 15r - 9(20) 20 15 9(20) 20 15 15 15-15 (3)(15) Solving for s s= 20 -r= 20-12 =8 Determine whether a segment is parallel to one side of a triangle. The first one is done for you Note that the illustrations are not drawn to scale. 1. Solution 2 (3), 2 (7) (11)(7) 48 YM YZ check whether YA YE 2" 48 56 48+ 16 56 + 21 2 11 43, 56 64 77 3 8 4 11 Therefore, MZ || AE Mathematics 9 S| Poge 'm,
Transcribed Image Text:2. Corresponding angles are 2. congruent. 3. ADAL - A KAM Similarity Theorem 3. 4. Definition of similar polygons 4. TRIANGLE PROPORTIONALITY THEOREM APPLICATION Solve for the unknown sides in the figures. The first one is done for you. Note that the figures are not drawn to scale. Solutions Solving for r 15r - 9(20) 20 15 9(20) 20 15 15 15-15 (3)(15) Solving for s s= 20 -r= 20-12 =8 Determine whether a segment is parallel to one side of a triangle. The first one is done for you Note that the illustrations are not drawn to scale. 1. Solution 2 (3), 2 (7) (11)(7) 48 YM YZ check whether YA YE 2" 48 56 48+ 16 56 + 21 2 11 43, 56 64 77 3 8 4 11 Therefore, MZ || AE Mathematics 9 S| Poge 'm,
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