Geometry Chapter 3 Vocabulary Quiz

Questions and Answers

What does the Angle Angle Triangle Similarity (AA ~) state?

Triangles with two pairs of equal angles are similar. (correct)

Triangles can be similar regardless of their angles.

Only triangles with one pair of equal angles are similar.

Triangles are similar if all three pairs of sides are proportional.

What does it mean for two shapes to be congruent?

Two shapes are congruent if they have exactly the same shape and size.

What is a proportional equation?

An equation stating that two ratios are equal.

What does the Side Angle Side Triangle Similarity (SAS ~) indicate?

Triangles are similar if two pairs of corresponding sides are proportional and have congruent included angles. Signup and view all the answers

What is a similarity statement?

A statement that indicates that two figures are similar. Signup and view all the answers

What does it mean to translate a figure?

A transformation that preserves the size, shape, and orientation of a figure while moving it to a new location. Signup and view all the answers

What are corresponding sides?

Sides in two or more figures that are images of each other with respect to a sequence of transformations. Signup and view all the answers

What is a flowchart?

A diagram showing an argument for a conclusion from certain evidence. Signup and view all the answers

What is a ratio?

A comparison of two quantities by division. Signup and view all the answers

What is a similarity transformation?

Movements of figures that preserve their shape, but not necessarily their size. Signup and view all the answers

What is a vertex?

A point where two or more line segments or rays meet to form a corner in a geometric shape. Signup and view all the answers

What is dilation in geometry?

A transformation which produces a figure similar to the original by proportionally shrinking or stretching it. Signup and view all the answers

What is the hypotenuse of a right triangle?

The longest side of a right triangle, opposite the right angle. Signup and view all the answers

What does perimeter refer to?

The distance around the exterior of a figure on a flat surface. Signup and view all the answers

What does it mean for two shapes to be similar?

Two shapes have the same shape but not necessarily the same size. Signup and view all the answers

What does the Side Side Side Triangle Similarity (SSS ~) state?

If two triangles have all three pairs of corresponding sides that are proportional, then the triangles are similar. Signup and view all the answers

What is the zoom factor?

The amount each side of a figure is multiplied by when the figure is proportionally enlarged or reduced in size. Signup and view all the answers

What is an angle in geometry?

An angle is formed by two rays joined at a common endpoint. Signup and view all the answers

What is a relationship in geometry?

A way that two objects, such as line segments or triangles, are connected. Signup and view all the answers

Study Notes

Triangle Similarity

Angle Angle Triangle Similarity (AA ~) states that if two angles in one triangle are congruent to two angles in another triangle, they are similar (e.g., ΔABC ~ ΔA'B'C').
Side Angle Side Triangle Similarity (SAS ~) requires two pairs of proportional sides and one congruent included angle for triangles to be similar.
Side Side Side Triangle Similarity (SSS ~) asserts that if all three pairs of corresponding sides in triangles are proportional, then the triangles are similar.

Congruence and Similarity

Congruent shapes have identical shapes and sizes, referred to as having a scale factor of 1.
Similar shapes share the same shape but can differ in size, with corresponding angles being congruent and sides being proportional.

Proportions and Ratios

A Proportional Equation denotes two equal ratios, essential for solving proportional problems.
A Ratio compares two quantities via division, expressible as a fraction or using a colon (e.g., 5:11).

Transformations

A Translation moves a figure to a new location while maintaining its size, shape, and orientation.
Similarity Transformations include rotations, reflections, translations, and dilations, preserving shape but not necessarily size.
Dilation involves proportionally scaling a figure from a specific point known as the point of dilation.

Geometric Elements

Corresponding Sides are sides in different figures that match images post transformations; congruent figures have congruent corresponding sides.
A Vertex is where two or more line segments or rays intersect, forming corners in polygons or edges in polyhedra.

Measurements

Perimeter is the total distance around a flat shape, calculated by summing the lengths of its sides; for circles, it's termed circumference.
The Hypotenuse is the longest side of a right triangle, always opposite the right angle.

Visual Tools

A Flowchart illustrates the logical progression toward a conclusion, using ovals and arrows to represent reasoning in proofs.
A Similarity Statement identifies the corresponding sides and angles of similar figures through the order of letters in their names.

Definitions Overview

Angle is formed by two rays at a common endpoint, often represented in geometric figures by segments meeting at a point.
Relationship describes the way two geometric objects, such as line segments or triangles, are interconnected.

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Description

Test your knowledge of key vocabulary from Geometry Chapter 3, focusing on angle-angle similarity in triangles. This quiz includes definitions and examples to help reinforce your understanding of triangle similarity concepts.