Midterm Geometry Review

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58 Terms

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Rigid Transformations

Transformations that do not change the shape or size of a geometric figure.

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Congruent Triangles

Triangles that are identical in shape and size.

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SAS

Side-Angle-Side; a method for proving triangle congruence.

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ASA

Angle-Side-Angle; a method for proving triangle congruence.

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SSS

Side-Side-Side; a method for proving triangle congruence.

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Proofs

Logical arguments that use deductive reasoning to show that a statement is true.

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Parallelograms

A quadrilateral with opposite sides that are parallel and equal in length.

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Dilations

Transformations that alter the size of a figure but maintain its shape.

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Similarity

Two figures that have the same shape but may differ in size.

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Pythagorean Theorem

c²=a²+b²

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Transversal Lines

Lines that cross at least two others at distinct points.

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Vertical Angles

Angles opposite each other when two lines intersect.

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Supplementary Angles

Two angles whose sum is 180 degrees.

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Complementary Angles

Two angles whose sum is 90 degrees.

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Segment Bisector

A line, ray, or segment that divides another segment into two equal parts.

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Angle Bisector

A ray that divides an angle into two equal angles.

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Axis of Symmetry

A line that divides a figure into two mirror-image halves.

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Exterior Angle Theorem

The theorem that states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.

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Dilation Scale Factor

The ratio that describes how much a figure is enlarged or reduced.

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Perpendicular Bisectors

Lines that cut another line segment into two equal parts at a 90-degree angle.

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Parallel Lines

Lines in a plane that never meet and are always the same distance apart.

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Supplementary Angles

Angles that add up to 180 degrees.

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Constructing Perpendicular Lines

Creating lines that intersect at a right angle.

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Symmetry

A property where one half of an object is a mirror image of the other half.

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90 Degree Rotation

Turning a shape to face a different direction, 90 degrees clockwise or counterclockwise.

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180 Degree Rotation

Turning a shape halfway around, resulting in an upside-down position.

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Line Segment

Part of a line that has two endpoints.

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Transformations

Operations that alter the position, size, or shape of a figure.

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Congruent Parts

Parts of figures that are equal in measure.

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Proportional Relationships

Relationships between quantities where one quantity is a constant multiple of the other.

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Scale Factor

The ratio that compares the size of a model to the size of the original figure.

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Triangle Congruence

A condition where two triangles are identical in size and shape.

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Constructing Angle Bisectors

Dividing an angle into two equal angles.

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Quadrilateral

A four-sided polygon.

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Similar Right Triangles

Right triangles that have the same shape but differ in size.

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Dilations in Geometry

Transformations that enlarge or reduce figures while preserving their proportions.

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Congruent Parts in Triangles

Corresponding sides and angles in congruent triangles that are equal in measure.

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Constructing Parallel Lines

Creating lines that are equidistant and never intersect.

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Triangle Properties

Characteristics and rules applicable to triangles, such as angle sum and congruence.

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Hypotenuse-Leg (HL) Theorem

A method for proving the congruence of two right triangles if the lengths of the hypotenuse and one leg are equal.

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Hypotenuse

The longest side of a right triangle, opposite the right angle.

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Leg of a Right Triangle

Either of the two shorter sides that form the right angle.

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Right Triangle

A triangle that has one angle measuring 90 degrees.

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Congruence Criteria for Triangles

Rules that determine when two triangles are congruent, including HL, SAS, SSS, and ASA.

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<p>Equilateral Triangle</p>

Equilateral Triangle

A triangle with all three sides of equal length.

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<p>Isosceles Triangle</p>

Isosceles Triangle

A triangle with at least two sides of equal length.

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<p>Scalene Triangle</p>

Scalene Triangle

A triangle with all sides of different lengths.

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<p>Acute Triangle</p>

Acute Triangle

A triangle with all angles measuring less than 90 degrees.

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<p>Obtuse Triangle</p>

Obtuse Triangle

A triangle that has one angle measuring more than 90 degrees.

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<p>Right Isosceles Triangle</p>

Right Isosceles Triangle

An isosceles triangle with a right angle.

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<p>30-60-90 Triangle</p>

30-60-90 Triangle

A special right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees.

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<p>45-45-90 Triangle</p>

45-45-90 Triangle

A special right triangle where the angles are both 45 degrees and the legs are equal.

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Area of Triangle

Calculated as 1/2 times the base times the height.

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Translation

A rigid transformation that slides a figure from one position to another without rotating or flipping it.

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Rotation

A rigid transformation that turns a figure about a fixed point.

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Reflection

A rigid transformation that flips a figure over a line, creating a mirror image.

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Rigid Motion

Another term for a rigid transformation, emphasizing that the figures retain their size and shape.

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Composition of Rigid Transformations

Applying multiple rigid transformations in sequence to a figure.