Marshak Geometry Final Review

What is the converse of the following statement:

If Joe goes fishing, then he needs bait.

• If he needs bait, then Joe goes fishing.

• If Joe does not go fishing, then he does not need bait.

• If he does not need bait, then Joe does not go fishing.

• If Joe goes fishing, the he does not need bait.

Answer explanation

The converse switches the order of the statement, the inverse makes both parts negative, and the contrapositive does both.

Line p is a transversal. For lines q, r, s, and t, which is not parallel to the other three?

• q

• r

• s

• t

Answer explanation

In order for lines to be parallel using angle pairs, angle values must be congruent or supplementary.

The diameter of a circle has endpoints (-3,2) and (3,-2). Which is closest to the length of the diameter of the circle?

• 1.4

• 3.2

• 7.2

• 10.0

Answer explanation

Plug the coordinates into the distance formula. Remember, for the final, you must know the coordinate geometry formulas!

Which is most likely a line of symmetry for triangle KLM?

• q

• r

• s

• t

Answer explanation

A line of symmetry is a line that you can fold your image over to get two perfect reflections of each other. A point of symmetry is where you can rotate your image and get the same image back.

What are the most likely coordinates of R` if R`S` is a reflection of RS across the y-axis

• (4,3)

• (-4,-3)

• (4,-3)

• (3,4)

Answer explanation

A reflection over the y-axis will negate the x value of the coordinate pair.

Which pipe lengths could be joined to form a triangle?

• 15, 6, 5

• 14, 12, 5

• 40, 20, 10

• 19, 16, 2

Answer explanation

To prove a set of values can make a triangle, use the inequality small+middle>big. To prove a set of values can make a right triangle, use the Pythagorean Theorem.

Which lists the angles of the triangle in order from least to greatest?

• <R, <Q, <P

• <Q, <P, <R

• <P, <R, <Q

• <P, <Q, <R

Answer explanation

The smallest angle is opposite the smallest side. The largest angle is opposite the largest side.

Given: M is the midpoint of LN and KP.

• Angle Side Angle (ASA)

• Side Side Side (SSS)

• Side Angle Side (SAS)

• Angle Angle Side (AAS)

Answer explanation

Since M is the midpoint of both segments, you will get two pairs of congruent sides. Where those two segments intersect is a pair of congruent vertical angles. That's why SAS is the best answer.

If PQ is parallel to ST, what is ST, the width of the lake?

• 62 m

• 72 m

• 84 m

• 98 m

Answer explanation

Since we know the triangle are similar, you will need a proportion to solve for the missing side.

• 24 ft

• 33 ft

• 35 ft

• 41 ft

Answer explanation

First, mark the height of the building as x. Since this problem involves a right triangle, with information about sides and angles, this is a trig question. You have opposite and adjacent, so use tan. tan70=x/12