Geometry Final PRACTICE TEST

• 23º

• 90º

• 46º

• 11.5º

Answer explanation

Remember that angle bisectors cut an angle into 2 CONGRUENT parts.

Angle MLP is half of the angle, so the measure of angle MLN must be double that.

What reason would support the 2nd statement?

• Addition POE

• Division POE

• Multiplication POE

• Subtraction POE

Answer explanation

To get from the first statement to the 2nd statement 3 had to be SUBTRACTED from both sides. Meaning that statement 2 is true because of the "subtraction property of equality"

Which is a description of the transformation shown to the right?

• 1. Translation down 4 and right 4

• 1. Translation up 3 and left 6

• 1. Translation down 3 and right 6

• 1. Translation up 4 and left 4

Answer explanation

Make sure you pay attention to which figure is the pre-image and which is the image.

The original ∆ is the one to the left, so the new ∆'s points each had to move right then down.

• 105º

• 75º

• 180º

• 255º

Answer explanation

Use triangle sum theorem (interior angles in a ∆ add to 180º) to find the 3rd interior angle of the triangle.

Then use the fact that <ACB and <ACD are a linear pair (add to 180º) to solve for <ACD

Answer explanation

<1 and <8 are alternate exterior angles to one another - meaning they are congruent in measurement.

• Corresponding Angles are Congruent

• Vertical Angles are Congruent

• Given

• Reflexive Property

Answer explanation

<3 and <7 must be congruent because they are in the same relative locations at their intersecting lines

In other words, they are "corresponding angles"

• Corresponding Angles

• Definition of Midpoint

• Vertical Angles are Congruent

• Definition of Segment Bisector

Answer explanation

You're told in the givens that R is the midpoint of PJ and ZT.

Since R is a midpoint of those segments we can state that the two parts each segment is split into must be congruent. Since that's what midpoints do!

Answer explanation

Remember the order of the letters tells you which parts correspond to which. If the ∆s are congruent the corresponding parts are as well.

Which of the following would be the FINAL reason in this proof?

• ASA (angle-side-angle)

• SAS (side-angle-side)

• AAS (angle-angle-side)

• CPCTC (corresponding parts of congruent ∆s are congruent)

Answer explanation

Remember that ∆ congruence theorems (ASA, SSS, AAS, etc.) can only be used to prove that triangles are congruent.

This proof is asking you to prove that PARTS of the triangles are congruent!

A 6 foot tall man is standing near a 72 foot tall lighthouse. The lighthouse casts a shadow that is 84 feet long. 

How long is the man's shadow?

• 7 feet

• 6 feet

• 18 feet

• 12 feet

Answer explanation

This is an example of similar triangles (or scale figures).

You can find the scale factor between the man and the lighthouse by dividing 72/8. This tells you the scale factor of enlargement is 12.

So the lighthouse's shadow is 12 time longer than the mans.

Then use this scale factor to work backwards to the man's shadow length.