Q23WE. For Exercises 23-27 write proofs... [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: Q23WE. (page 157)

For Exercises 23-27 write proofs in paragraph form. (Hint: You can use theorems from this section to write fairly short proofs for Exercises 23 and 24.)
23. Given: $\overset{鈫�}{S R}$ is the $鈯�$ bisector of $\overset{炉}{Q T}; \overset{鈫�}{Q R}$ is the $鈯�$ bisector of $\overset{炉}{S P}$
Prove: $P Q = T S$

Short Answer

Expert verified

Since, $\overset{鈫�}{Q R}$ is the perpendicular bisector of $\overset{炉}{P S}$ , so the point $Q$ is equidistance from endpoints $P$ and $S$ that is $P Q = Q S$ . Also, $\overset{鈫�}{S R}$ is the perpendicular bisector of $\overset{炉}{Q T}$ , so the point $S$ is equidistance to endpoints $Q$ and $T$ that is $Q S = T S$ . By using reflexive property,

$P Q = Q S and Q S = S T$ implies $P Q = T S$ .

Step by step solution

Step 1. Show that PQ=QS.

Since, $\overset{鈫�}{Q R}$ is the perpendicular bisector of $\overset{炉}{P S}$ , so the point $Q$ is equidistance from endpoints $P$ and $S$ . Thus $P Q = Q S$

Step 2. Show that QS=ST.

Since, $\overset{鈫�}{S R}$ is perpendicular bisector of role="math" localid="1649243006755" $\overset{炉}{Q T}$ , so point role="math" localid="1649243017087" $S$ is equidistance from endpoints $Q$ and $T$ . Thus $Q S = T S$

Step 3. Use reflexive property.

By using reflexive property, for real numbers $a, b$ and role="math" localid="1649242924111" $c$ . if

$a = b and b = c$ then $a = c$

So $P Q = Q S and Q S = S T$ implies $P Q = T S$

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91影视

Short Answer

Step by step solution

Step 1. Show that PQ=QS.

Step 2. Show that QS=ST.

Step 3. Use reflexive property.

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91影视

For Exercises 23-27 write proofs in paragraph form. (Hint: You can use theorems from this section to write fairly short proofs for Exercises 23 and 24.)23. Given:SR鈫�is the 鈯�bisector ofQT炉;QR鈫�is the鈯�bisector ofSP炉Prove:PQ=TS

Short Answer

Step by step solution

Step 1. Show that PQ=QS.

Step 2. Show that QS=ST.

Step 3. Use reflexive property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.