Title: Chapter 5 Free Response
Course: quiz duplicate error

Identify all the parallel segments in the diagram.
[Image]

B is the midpoint of [Image] and D is the midpoint of [Image] Solve for x,given [Image] and [Image]
[Image]

Given: [Image] is the perpendicular bisector of IK. Name two lengths that are equal.
[Image]

In [Image] draw median FJ from F to the side opposite F.
[Image]

Write the inverse of this statement:
If a number is divisible by two, then it is even.

To prove “p is equal to q” using an indirect proof, what would your starting assumption be?

Complete the indirect proof.

Given: Bobby and Kina together hit at least 30 home runs. Bobby hit 18 home runs.
Prove: Kina hit at least 12 home runs.

Assume Kina hit a.___ than 12 home runs. This means Bobby and Kina combined to hit at most b.____ home runs. This contradicts the given information that c. _____. The assumption is false. Therefore, Kina d. ______.

Complete the indirect proof.

Given: Rectangle JKLM has an area of 36 square centimeters. Side [Image] is at least 4 centimeters long.
Prove: KL£ 9 centimeters

Assume that a. ____. Then the area of rectangle JKLM is greater than b. _____ , which contradicts the given information that c. _____. So the assumption must be false. Therefore, d. _____.

Given points A(2, 3) and B(–2, 5),explain how you could use the Distance Formula and an indirect argument to show that point C(0, 3) is NOT the midpoint of [Image].

Can these three segments form the sides of a triangle? Explain.

[Image]

Li went for a mountain-bike ride in a relatively flat wooded area. She rode for 6 km in one direction and then turned and pedaled 16 km in another. Finally she turned in the direction of her starting point and rode 8 km. When she stopped, was it possible that Li was back at her starting point? Explain.

Write a paragraph proof.

Given: [Image]
Prove: [Image]
[Image]

If AC = 18 and BD = 21, find the perimeter of the small quadrilateral inside quadrilateral ABCD. Explain. Based on your work, make a conjecture about the relationship between the “midsegment quadrilateral” and the diagonals of the large quadrilateral.
[Image]

AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.
[Image]

The Allards put their dog Pepper on an adjustable-length leash. They tie the other end of the leash to an anchor in their triangular yard. The anchor allows Pepper to roam a complete circle. Where should the Allards install the anchor to keep Pepper in their yard but also make Pepper’s circle as large as possible? Then how long should they make the leash? Explain your answers.

Use indirect reasoning to explain why a quadrilateral can have no more than three obtuse angles.

Keegan knows that the statement “if a figure is a rectangle, then it is a square” is false, but he thinks the contrapositive is true. Is he correct? Explain.

A conditional statement and its contrapositive have the same truth value and are called equivalent statements. How are the inverse and converse of a conditional statement related to each other?

T is the midpoint of QR. U is the midpoint of QS. RS = 36 and mÐQUT = 85. What are TU and mÐQSR? Explain.
[Image]

Find EF and DG. For each length, explain your answer. If you cannot determine the length of one or both of the segments, write not enough information.
[Image]

A tennis court has a baseline at each end. One is labeled in the picture. Which part of the tennis court is equidistant from the midpoints of the two baselines? Explain.
[Image]

Explain why this is true: “Any three noncollinear points lie on a circle.”

Explain why [Image]
[Image]

P, Q, and R are three different points. PQ = 3x + 2, QR = x, and RP = x + 2, and [Image].. List the angles of ΔPQR in order from largest to smallest and justify your response.

Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.