Title: Midyear Free Response
Course: quiz duplicate error

On a number line, P has coordinate –47 and Q has coordinate 40. Find PQ.

For [Image] and [Image], [Image], [Image], and [Image]. Explain how you can prove [Image] by ASA.

Can you conclude the triangles are congruent? Justify your answer.
[Image]

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

Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.

Is [Image] by HL? If so, name the legs that allow the use of HL.
[Image]

Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.

If the probability that an event will occur is 0, then the event is impossible to occur.

Fill in each missing reason.

Given: [Image]
[Image]

[Image]

Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that [Image].
[Image]

For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Explain.

A straight angle has a measure of 180.
[Image] is a straight angle.

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

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not possible. Explain.

Statement 1: If two lines intersect, then they are not parallel.
Statement 2: [Image] do not intersect.

For the two quadrilaterals below, [Image] [Image] [Image] and [Image] Complete this congruence statement for the two quadrilaterals.
[Image] ___?___

[Image]

You live in Salt Lake City, Utah, which has approximate (latitude, longitude) coordinates of (41N, 112W). Your friend lives in Goodwin, Arkansas, with coordinates of (35N, 91W). You plan to meet halfway between the two cities. Find the coordinates of the halfway point.

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

All of the angles of a quadrilateral are congruent. Can the quadrilateral be a parallelogram? Explain.

Isosceles trapezoid ABCD has legs [Image] and [Image] and base [Image] If AB = 4y – 3, BC = 3y – 4, and CD = 5y – 10, find the value of y.

Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.
[Image]

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

Give a convincing argument that quadrilateral ABCD with A(–3, –4), B(0, –2), C(6, –2), and D(3, –4) is a parallelogram.

Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
[Image]

a. Write the following conditional in if-then form.
b. Write its converse in if-then form.
On a number line, the points with coordinates –2 and 5 are 7 units apart.

What type of quadrilateral has exactly one pair of parallel sides?

Is the quadrilateral a parallelogram? Explain. The diagram is not to scale.
[Image]

Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle.

Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a good definition. Explain.

Three points are collinear if and only if they are coplanar.

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

Line p contains points A(–1, 4) and B(3, –5). Line q is parallel to line p. Line r is perpendicular to line q. What is the slope of line r? Explain.

It appears from the name of the HL Theorem that you actually need to know that only two parts of two triangles are congruent in order to prove two triangles congruent. Is this the case?

For parallelogram PQRS, find the values of x and y. Then find PT, TR, ST, and TQ. The diagram is not to scale.
[Image]

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