Geometry and Measurement: Congruence, Transformations, and Circles

Similar

Same shape, different size; matching angles, proportional sides.

Congruent

Same shape and same size.

Included Angle

The angle formed between two given sides.

Hypotenuse

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

Leg

One of the two sides that form the right angle in a right triangle.

Angle Bisector

A line or ray that splits an angle into two equal angles.

Perpendicular Bisector

A line that cuts a segment in half and forms a right angle with it.

Circumscribed

A circle drawn around a shape, touching all its vertices.

Rhombus

A four-sided shape with all sides equal in length.

Transformation

A change made to a figure (move, flip, turn, or resize).

Isometry

A transformation that keeps the shape and size the same.

Image

The new figure after a transformation.

Translation (Slide)

A move that shifts a figure the same distance in the same direction.

Pre-Image (Original)

The figure before the transformation.

Slide Arrow (Vector)

An arrow showing the direction and distance of a slide.

Slide Line

A line showing the direction a figure slides along.

Rotation (Turn)

A turn of a figure around a point.

Turn Center

The point the figure turns around.

Turn Arrow

Arrow showing the direction of the turn.

Turn Angle (degree)

How far the figure turns (measured in degrees).

Tessellation (Repeated Filling)

A pattern that covers a surface with no gaps or overlaps.

Reflection (Flip)

A flip of a figure over a line.

Reflecting Line

The line the figure is flipped across.

Orientation

The direction a figure faces.

Angle of Incidence

The angle the original part of the figure makes when meeting the mirror line.

Angle of Reflection

The matching angle the reflected part makes on the other side.

Glide Reflection (Translate and Reflect)

A slide followed by a flip.

Dilation (Shrink, Grow)

A transformation that changes the size of a figure.

Center

The fixed point the figure expands or shrinks from.

Scale Factor

How much the figure is enlarged or reduced.

Measurement

Comparing something to a unit to find out how long, wide, or tall it is.

Non-Standard Units of Measure

Units that aren't commonly used or agreed on (e.g., hand spans, paperclips).

English System

Measurement system using inches, feet, yards, miles, etc.

Metric System

Measurement system based on powers of ten (millimeters, centimeters, meters, kilometers).

Base Unit

The main unit used for measuring a type of quantity (meter for length, gram for mass).

Greatest Possible Error (GPE)

The largest amount a measurement could be off, usually half the size of the measuring unit.

Dimensional Analysis

A method for converting between units by multiplying with conversion ratios.

Perimeter

The distance around a shape.

Circumference

The distance around a circle.

Diameter

A line across the circle through the center; equal to two radii.

Arc

A curved part of a circle's circumference.

Shadow of Person/Height of Person

= Shadow of Object/Height of Object

Arc Length

= 2πr(ፀ/360)