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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 25 and 26, supply the missing statements and reasons.

Given: Quadrilateral PQST with midpoints A, B, C, and D of the sides
Prove: ABCD is a

PROOF
Statements Reasons
1. Quadrilateral PQST with midpoints A, B, C, and D of the sides 1. ?
2. Draw T Q ¯ 2. Through two points, there is one line
3. A B ¯ | | T Q ¯  in  T P Q 3. The line joining the midpoints of two sides of a triangle is | | to the third side
4. D C ¯ | | T Q ¯  in  T S Q 4. ?
5. A B ¯ | | D C ¯ 5. ?
6. Draw P S ¯ 6. ?
7. A D ¯ | | P S ¯  in  T S P 7. ?
8. B C ¯ | | P S ¯  in  P S Q 8. ?
9. A D ¯ | | B C ¯ 9. ?
10. ? 10. If both pairs of opposite sides of a quadrilateral are | | , the quadrilateral is a

To determine

To supply:

The missing statements and reasons and prove ABCD is a .

Explanation

ASA Rule for triangle congruency:

Calculation:

Consider the quadrilateral.

The inner parallelogram creates four separate triangles. We must prove that the triangles opposite each other a congruent.

PROOF
Statements Reasons
1. Quadrilateral PQST with midpoints A, B, C, and D of the sides 1. Given
2. Draw TQ¯ 2. Through two points, there is one line
3. AB¯||TQ¯ in TPQ 3. The line joining the midpoints of two sides of a triangle is || to the third side
4. DC¯||TQ¯ in TSQ 4. The line joining the midpoints of two sides of a triangle is || to the third side. By ASA (Angle Side Angle), the opposite triangles are congruent.
5. AB¯||DC¯ 5

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