Math Chapter 4 Test: Geometry Flashcards

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Questions and Answers

What type of triangle has no congruent sides?

Equilateral

Scalene (correct)

Isosceles

Acute

What type of triangle has 2 congruent sides?

Obtuse

Isosceles (correct)

Equilateral

Scalene

What is the definition of an equilateral triangle?

All sides are congruent

What defines a right triangle?

Has one right angle Signup and view all the answers

What is a feature of an acute triangle?

Three acute angles Signup and view all the answers

What characterizes an obtuse triangle?

One obtuse angle Signup and view all the answers

What does an equiangular triangle possess?

Three congruent angles Signup and view all the answers

What is the distance formula?

Square root of (x2 - x1)^2 + (y2 - y1)^2 Signup and view all the answers

What types of angles exist?

Interior and exterior Signup and view all the answers

What is the acute angles relationship in a right triangle?

The acute angles are complementary. Signup and view all the answers

What are the congruence postulates?

All of the above Signup and view all the answers

What does SSS stand for?

If three sides of one triangle are congruent with three sides of another triangle, then they are congruent. Signup and view all the answers

What does the SAS postulate state?

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Signup and view all the answers

What is the hypothesis of the hypotenuse-leg congruence theorem?

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another, the triangles are congruent. Signup and view all the answers

What does the ASA postulate state?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then they are congruent. Signup and view all the answers

What does AAS indicate?

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then they are congruent. Signup and view all the answers

What can one conclude about an isosceles triangle with two congruent base angles?

The legs are congruent. Signup and view all the answers

What is the definition of a base angles theorem?

If two angles of a triangle are congruent, the sides opposite them are also congruent. Signup and view all the answers

What characterizes an equilateral triangle?

Congruent angles and sides. Signup and view all the answers

Can you not have enough information to conclude properties of a triangle?

True Signup and view all the answers

What is the translation formula?

(x,y) ---> (x+a, y+b) or subtract. Signup and view all the answers

What is the reflection formula over the x-axis?

(x,y) ---> (x, -y) Signup and view all the answers

What is the reflection formula over the y-axis?

(x,y) ---> (-x, y) Signup and view all the answers

Study Notes

Triangle Types

Scalene Triangle: No congruent sides.
Isosceles Triangle: Two congruent sides.
Equilateral Triangle: All sides are congruent.
Right Triangle: Contains one right angle.
Acute Triangle: All angles are acute.
Obtuse Triangle: Contains one obtuse angle.
Equiangular Triangle: All angles are congruent.

Theorems and Formulas

Distance Formula: Calculated as √((x₂ - x₁)² + (y₂ - y₁)²).
Exterior Angles: Angles outside of a polygon formed by extending a side.
Exterior Angle Theorem: The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.
Corollary to Triangle Sum Theorem: In a right triangle, the acute angles are complementary (A + Angle B = 90°).
Third Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle, the third angles are also congruent.

Transformations

Transformation: Movement or alteration of a figure to create a new figure.
Rigid Motions: Transformations that maintain the shape’s size and angles, preserving length, angle measure, and area.
Examples of Rigid Motions:
- Translation: Sliding the figure without rotation or flipping.
- Reflection: Flipping the figure over a line.
- Rotation: Turning the figure around a point.

Congruence Postulates

Congruence Postulates: Criteria to determine triangle congruence.
- SSS (Side-Side-Side): Three sides of one triangle are congruent to three sides of another.
- SAS (Side-Angle-Side): Two sides and the included angle of one triangle are congruent to those of another.
- HL (Hypotenuse-Leg): The hypotenuse and a leg of a right triangle are congruent to those of another right triangle.
- ASA (Angle-Side-Angle): Two angles and the included side of one triangle correspond to two angles and the included side of another.
- AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are congruent to those of another.

Special Properties

Base Angles Theorem: In an isosceles triangle, if two base angles are congruent, the legs of the triangle are also congruent.
Equilateral Triangle: All sides and angles are congruent, leading to a perfectly symmetric shape.

Transformation Formulas

Translation Formula: Given as (x,y) transforms to (x+a, y+b), where a and b are the horizontal and vertical shifts, respectively.
Reflection Formula Over X-axis: (x,y) transforms to (x, -y).
Reflection Formula Over Y-axis: (x,y) transforms to (-x, y).

Additional Notes

Lack of sufficient information may prevent conclusive analysis of certain triangle properties or orientations.

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Test your understanding of geometry terms with these flashcards from Math Chapter 4. Each card defines key concepts related to different types of triangles and their properties. Perfect for reviewing before a test or enhancing your math vocabulary.