Q29. Write paragraph proofs. (In this... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q29. (page 158)

Write paragraph proofs. (In this book a star designates an exercise that is unusually difficult.)
Given: $\overset{鈫�}{A M}$ is the $鈯�$ bis. of $\overset{炉}{B C}$ ; $\overset{炉}{A E} 鈯� \overset{炉}{B D}; \overset{炉}{A F} 鈯� \overset{炉}{D F}; 鈭� 1 鈮� 鈭� 2$
Prove: $\overset{炉}{B E} 鈮� \overset{炉}{C F}$

Short Answer

Expert verified

Since, $鈭� A E D 鈮� 鈭� A F D$ as each angle is of $90 掳$ and $\overset{炉}{A D} 鈮� \overset{炉}{A D}$ by using reflexive property. Thus, using given statement $鈭� 1 鈮� 鈭� 2$ , $螖 A E D 鈮� 螖 A F D$ by AAS (Angle-Angle-Side) Postulate. As corresponding parts of congruent triangle are congruent implies $\overset{炉}{A E} 鈮� \overset{炉}{A F}$ . Since, point $A$ lies on the perpendicular bisector of $\overset{炉}{B C}$ . Therefore, point $A$ is equidistant from endpoints of $\overset{炉}{B C}$ meaning $\overset{炉}{A B} 鈮� \overset{炉}{A C}$ . As one leg and hypotenuse of a right triangle is congruent to corresponding leg and hypotenuse of other right triangle. So by HL Theorem, $螖 A E B 鈮� 螖 A C F$ . As corresponding parts of congruent triangle are congruent implies $\overset{炉}{B E} 鈮� \overset{炉}{C F}$

Step by step solution

Step 1. Show AE¯≅AF¯.

Step 2. Show AB¯≅AC¯.

Since, point $A$ lies on the perpendicular bisector of $\overset{炉}{B C}$

Therefore, point $A$ is equidistant from endpoints of $\overset{炉}{B C}$ meaning $\overset{炉}{A B} 鈮� \overset{炉}{A C}$

Step 3. Show BE¯≅CF¯.

From above two steps, $\overset{炉}{A E} 鈮� \overset{炉}{A F}$ and $\overset{炉}{A B} 鈮� \overset{炉}{A C}$ .

As one leg and hypotenuse of a right triangle is congruent to corresponding leg and hypotenuse of other right triangle. So by HL Theorem, $螖 A E B 鈮� 螖 A C F$ . As corresponding parts of congruent triangle are congruent implies $\overset{炉}{B E} 鈮� \overset{炉}{C F}$

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91影视

Short Answer

Step by step solution

Step 1. Show AE¯≅AF¯.

Step 2. Show AB¯≅AC¯.

Step 3. Show BE¯≅CF¯.

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91影视

Write paragraph proofs. (In this book a star designates an exercise that is unusually difficult.)Given: AM鈫�is the 鈯�bis. of BC炉;AE炉鈯�BD炉;AF炉鈯�DF炉;鈭�1鈮�鈭�2Prove:BE炉鈮�CF炉

Short Answer

Step by step solution

Step 1. Show AE¯≅AF¯.

Step 2. Show AB¯≅AC¯.

Step 3. Show BE¯≅CF¯.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.