Congruent TrianglesIntroduction to

congruent angles

Polygon

• a closed plane figure formed by three or more segments that do not cross

Congruent

• having the same size or angle measure.

• The symbol for congruent is So, the symbol, stands for “is congruent to.”

Congruent Polygons

• polygons with the same size AND shape.

C

A B

F

GE

FGECAB

Corresponding Parts

• parts of polygons that are matching and congruent.

____CAC

A B

F

GE

___CBAFG FEG

Need to Know!

**When stating congruent sides, the order that the segments are written in is very important, because it will identify direction.

Polygons and Quadrilateral

s What are the differences?

Quadrilateral

• a FOUR sided polygon.

Name some quadrilaterals?Square

Rectangle

Rhombus/ Diamond

Parallelogram

Trapezoid

Pentagon

• a FIVE sided polygon.

What famous building houses the various armed forces?

The Pentagon

Hexagon

• a SIX sided polygon.

Octagon

• an EIGHT sided polygon.

Name a common object that has this shape.

stop sign

Decagon

• a TEN sided polygon.

Regular Polygon

• a polygon with ALL sides congruent and ALL angles congruent.

Name a regular polygon that is:

a triangle –

a quadrilateral –

Equilateral TriangleSquare

Parallel Lines

• two lines that lie in the same plane (a flat surface) and DO NOT intersect

Trapezoid

quadrilateral with exactly one pair of parallel sides

Parallelogram

• quadrilateral with both pairs of opposite sides parallel

Rectangle

• a parallelogram with 4 right angles

Rhombus

• a parallelogram with 4 congruent sides

Square• a parallelogram with 4 right

angles and 4 congruent sidesWhat other names can a square have?

quadrilateral

parallelogram

rectangle

rhombus

Can a rectangle be a square?

Yes, but not always.

When?

Only if all 4 sides are also congruent.

Can a rhombus be a square?

Yes, but not always

When?

if all 4 angles are right angles.

Can a trapezoid be a rectangle?

NO

Why?

Trapezoid can have only 1 set of parallel sides. Rectangle has 2.

Is a rectangle always a parallelogram?

Yes, by its definition.

a parallelogram with 4 right angles

Is a square always a rectangle?

Yes, ALWAYS!

It fits the definition of a rectangle because a square is a parallelogram, and has 4 right angles.

Is a rectangle always a square?

NO

Only if the rectangle also has 4 congruent sides.

Diagonal

• the segment that connects two corners of a polygon, but does not make a side of the polygon.

• diagonals connect the inside of a polygon

Circles

Almost there…

Circle

• the set of points in a plane that are all the same distance from a given point, called the center.

• a circle is named by its center

Radius

• a segment from the center of a circle to a point on the circle.

• The plural form of radius is radii.

Diameter

• a segment that passes through the center of a circle and has both endpoints on the circle.

Chord

• a segment that has both endpoints on the circle.

Central Angle

• an angle with its vertex at the center of a circle.

Arc

• a part of a circle (along the outside of the circle)

• named using just 2 letters

Semicircle

• a half of a circle.

• named using 3 letters–Why 3 letters?

Compass

• a geometric tool used to draw circles and arcs.

Inscribed Polygon

• a polygon whose sides are chords of a circle.

A chord is always a diameter.

True or False?

FALSE!

not always, a chord IS a diameter, IF, it also passes through the center of the circle

A diameter is always chord.

True or False?

TRUE!

by definition, a diameter has two endpoints on the circle.

A diameter is equal, in length, to two radii.

True or False?

TRUE!

diameter is equal to the radius times 2.

A radius can be a chord.

True or False?

FALSE!

only 1 part of a radius touches the circle, not two endpoints.

Identify!

B

F

A

CD

E

G