Geometry Assessment Quiz

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Questions and Answers

What theorem is used to establish the similarity between triangles XY Z and ABC?

Pythagorean Theorem

Triangle Inequality Theorem

Side-Side-Side Theorem

Angle-Angle Similarity Theorem (correct)

Triangle XY Z and triangle ABC are proven similar using the Side-Angle-Side Theorem.

False (B)

What is the length of the smaller support beam BD in feet?

In the ski jump problem, the lengths of the ramp segments AD and DE are _ feet and _ feet respectively.

15, 10 Signup and view all the answers

Match the following segments with their respective lengths:

AD = 15 feet DE = 10 feet BD = 12 feet CE = unknown Signup and view all the answers

How far is the model satellite from the center of the Earth model, to the nearest inch?

8 inches (A) Signup and view all the answers

Angles ABC and EDC are acute angles.

False (B) Signup and view all the answers

What is the distance in inches from the center of the Moon model, B, to the base, A?

4 inches Signup and view all the answers

The distance from the center of the Earth model, D, to the launch site, E, is _____ inches.

6 Signup and view all the answers

Which set of angles constitutes the measures of angles ABC and EDC?

35°, 110°, 45° (A) Signup and view all the answers

Given the endpoints (−2, 6) and (4, 3), what is the midpoint of the line segment?

(1, 4.5) Signup and view all the answers

The center of dilation for the triangle M N O is located at the _____.

origin Signup and view all the answers

Match the following properties to their definitions:

Right angle = An angle measuring 90 degrees Midpoint = The point that divides a segment into two equal parts Dilation = A transformation that produces an image that is the same shape as the original Segment = A part of a line bounded by two distinct endpoints Signup and view all the answers

Which reason completes the two-column proof regarding triangle similarity?

Angle-Angle Similarity Theorem (B) Signup and view all the answers

Which counterexample shows that triangles T U W and W XT are NOT similar?

∠U ≅ ∠X, but ∠U T W is not congruent to ∠XW T. (D) Signup and view all the answers

The Triangle Sum Theorem states that the sum of the angles in a triangle is equal to 180 degrees.

True (A) Signup and view all the answers

What type of triangle transformation is described when a triangle is changed in size while maintaining its shape?

dilation Signup and view all the answers

In order to establish that triangles are similar, it is sufficient to show that two pairs of _____ are congruent.

angles Signup and view all the answers

Which theorem can be used to claim triangle similarity through angle congruence?

Angle-Angle Similarity Theorem (C) Signup and view all the answers

Match the following triangle similarity criteria with their descriptions:

Angle-Angle = Two angles of one triangle are congruent to two angles of another triangle. Side-Angle-Side = Two sides are in proportion and the included angle is congruent. Side-Side-Side = All three sides of one triangle are in proportion to the corresponding sides of another triangle. Signup and view all the answers

Describe what it means for two triangles to be similar.

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are in proportion. Signup and view all the answers

Flashcards

Angle-Angle Similarity Theorem

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Perimeter of Triangle

The perimeter is the total length of all sides of a triangle, calculated as the sum of its side lengths.

Parallel Lines

Parallel lines are lines in a plane that never intersect and are always the same distance apart.

Triangle Similarity in Geometry

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.