Exam Review

Use the Law of Detachment to draw a conclusion from the two given statements. If

not possible, write, not possible.

• I will lose weight if I eat a lot of vegetables.

• I lost weight.

Write the two statements that make up the following biconditional.

• I go to school if and only if my students make me.

Write the converse of the conditional:

• If a number is divisible by 10, then it is divisible by 5.

Complete the the statement:

• If a transversal intersects two parallel planes, then the…– …alternate interior angles are _____– …the same side interior angles are _____– …the same side exterior angles are ___– …the corresponding angles are ___

Exterior angles

• The sum of the measures of two exterior angles of a triangle are 302 degrees. What is the measure of the third exterior angle?

Contrapositive

• Mrs. Thelen knows that the conditional “if students pay attention and come to school in Geometry, then they will do well.” Is the contrapositive true or false? Why?

Converse

Conditional: If x = 5, then x2 = 25.

What is the truth value of the conditional?

Write the converse.

What is the truth value of the converse?

Regular Polygon

• Find the measures of an interior angle and an exterior angle of a regular heptagon.

Triangle Interior Angle Measures

• Find the values of u an v

x y

32°

Point-Slope form

• Write an equation of a line in point-slope form that passes through the point (-5, 7) and has a slope of –4.

Isosceles Triangle

• The legs of an isosceles triangle have lengths 5x –10 and 4x + 2. The base has a length of 40x. What is the length of the base?

Find the values of u and v

132°

4y

2x

Circumference and Area

• Find the exact area and exact circumference of the circle below:

Angle Bisector

• Solve for x and the angle measure

5x - 2

4x + 14

Name the smallest angle of the triangle below

State the conclusions for the proof:

• M<ABC + m<BCD = M<ABD _____

• 3x + 4(x –2) = 132 _____

• 3x + 4x – 8 = 132____

• 7x – 8 = 132 ____

• 7x = 132

• x = 19

Interior angles of a Parallelogram

If m<1 is 42 degrees and m <2 = 58 degrees, then what is the measure of <DCB?

Indirect Proof

Given: Triangle ABC is o

Name a pair of opposite rays

If AM = 5x + 2 and MB = 3x –2 and AB = 42, find x and MB

Triangle Inequality

• Two sides of a triangle are 5 and 11. What lengths are possible for the third side? Write your answer in the form of a compound inequality.

Distance

• Find the distance between points (4,5) and (-2, -6)

Counterexample

• Give a counterexample to the statement:

“If you live in Grand Rapids, then you live in Michigan”

Triangle Interior Angles

Write and solve an equation to find x.

Classify the triangle

• Classify a triangle with sides 5, 6, 7 by the number of sides.

• Classify a triangle with angle measures 42, 48, and 90 by angle measure.

Graph in standard form:

• Graph in standard form by using x and y intercepts:

6x – 3y = 24

Triangle Proofs

• What other information do you need in order to prove the triangles below are congruent?

Triangle Congruence Proofs

• From the information, can you prove that the two triangles at right are congruent?

Given: M is the midpoint of the segment QT

• Why or why not?

Triangle Midsegments

• Find x.

Inverse

Write the inverse of the statement:

If I go to bed early, then I am happy in the morning.

Which statements contradict eachother?

• Triangle ABC is obtuse

• M < A = 102 degrees

• A, B, and C are collinear

Quadrilateral – Venn Diagram

• Which Venn Diagram is correct?

Be able to construct:

• Angle bisector

• Perpendicular bisector

• Parallel lines