Geometry Chapter 5 Review

Is the inverse true?

If a triangle has three congruent sides, then it is equiangular.

Is the contra-positive true?

If a triangle has three congruent sides, then it is equiangular.

Is the inverse true?

If an isosceles triangle is obtuse, then its vertex angle is obtuse.

Is the contra-positive true?

If an isosceles triangle is obtuse, then its vertex angle is obtuse.

Is the inverse true?

If two lines are parallel, then they do not intersect.

Is the contra-positive true?

If two lines are parallel, then they do not intersect.

Midsegment

When a triangle’s sides are cut by medians, the relationship to the opposite side is _____.

Midsegment

If a triangle’s midsegment measurement is x, the opposite side’s measurement is _____.

Identify the contradiction.

I. Angles A and B are acute angles.II. Angle A = 45°.III. Angles A and B are supplementary.

Identify the contradiction.

ABCD is a quadrilateral.ABCD is a square.Angle A > Angle D.

True or False and Explain

An equilateral triangle cannot have a right angle.

Explain

The base of an isosceles triangle has a length of 10 feet. What can you say about the length of the legs?

Explain

Two sides of a triangle have lengths of 12 and 18. What can you say about the length of the third side? It can be any number between ____ and ____. How do you know?

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The circumcenter of a right triangle lies inside, outside, or on the triangle?

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The largest angle of a triangle is the angle opposite the __________ _________.

Circumcenter

Find the center of the circle that circumscribes the triangle plotted at the following points:(-7, 3), (9, 3), and (-7, -7).

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A _______ is from a vertex and cuts the opposite side of a triangle in half.

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A ________ is from a vertex meeting the opposite side of a triangle at a 90° angle.

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A _________ cuts a segment into two congruent parts at a right angle.

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The ____________ of a statement has the opposite truth value.

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Two collinear rays with the same endpoint are known as a ____________.

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The medians of a triangle are concurrent at a point called the __________________.

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A ____________ angle has a measure between 90 and 180.

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Coplaner lines that do not intersect are called _________ lines.

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Noncoplaner lines that do not intersect are called _________ lines.

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A ________ triangle has one angle formed by perpendicular lines.

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The point of concurrency (intersection) of the perpendicular bisectors of a triangle is the ____________________.

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The point of concurrency (intersection) of the altitudes of a triangle is the ____________________.

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The point of concurrency (intersection) of the medians of a triangle is the ____________________.