exam review. use the law of detachment to draw a conclusion from the two given statements. if not...
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Exam Review
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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.
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Write the two statements that make up the following biconditional.
• I go to school if and only if my students make me.
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Write the converse of the conditional:
• If a number is divisible by 10, then it is divisible by 5.
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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 ___
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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?
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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?
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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?
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Regular Polygon
• Find the measures of an interior angle and an exterior angle of a regular heptagon.
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Triangle Interior Angle Measures
• Find the values of u an v
x y
32°
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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.
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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?
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Find the values of u and v
132°
4y
2x
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Circumference and Area
• Find the exact area and exact circumference of the circle below:
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Angle Bisector
• Solve for x and the angle measure
5x - 2
4x + 14
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Name the smallest angle of the triangle below
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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
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Interior angles of a Parallelogram
If m<1 is 42 degrees and m <2 = 58 degrees, then what is the measure of <DCB?
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Indirect Proof
Given: Triangle ABC is o
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Name a pair of opposite rays
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If AM = 5x + 2 and MB = 3x –2 and AB = 42, find x and MB
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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.
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Distance
• Find the distance between points (4,5) and (-2, -6)
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Counterexample
• Give a counterexample to the statement:
“If you live in Grand Rapids, then you live in Michigan”
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Triangle Interior Angles
Write and solve an equation to find x.
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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.
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Graph in standard form:
• Graph in standard form by using x and y intercepts:
6x – 3y = 24
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Triangle Proofs
• What other information do you need in order to prove the triangles below are congruent?
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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?
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Triangle Midsegments
• Find x.
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Inverse
Write the inverse of the statement:
If I go to bed early, then I am happy in the morning.
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Which statements contradict eachother?
• Triangle ABC is obtuse
• M < A = 102 degrees
• A, B, and C are collinear
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Quadrilateral – Venn Diagram
• Which Venn Diagram is correct?
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Be able to construct:
• Angle bisector
• Perpendicular bisector
• Parallel lines