Congruent Triangles

1
Congruent Triangles

• Introduction to congruent angles

2
Polygon

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

3
Congruent

• having the same size or angle measure.
• The symbol for congruent is So, the symbol,
  stands for is congruent to.

4
Congruent Polygons

• polygons with the same size AND shape.

5
Corresponding Parts

• parts of polygons that are matching and congruent.

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Need to Know!

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

7
Polygons and Quadrilaterals

• What are the differences?

8
Quadrilateral

• a FOUR sided polygon.
• Name some quadrilaterals?
• Square
• Rectangle
• Rhombus/ Diamond
• Parallelogram
• Trapezoid

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Pentagon

• a FIVE sided polygon.
• What famous building houses the various armed
  forces?
• The Pentagon

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Hexagon

• a SIX sided polygon.

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Octagon

• an EIGHT sided polygon.
• Name a common object that has this shape.
• stop sign

12
Decagon

• a TEN sided polygon.

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Regular Polygon

• a polygon with ALL sides congruent and ALL angles
  congruent.
• Name a regular polygon that is
• a triangle
• a quadrilateral

Equilateral Triangle
Square
14
Parallel Lines

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

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Trapezoid

• quadrilateral with exactly one pair of parallel
  sides

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Parallelogram

• quadrilateral with both pairs of opposite sides
  parallel

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Rectangle

• a parallelogram with 4 right angles

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Rhombus

• a parallelogram with 4 congruent sides

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Square

• a parallelogram with 4 right angles and 4
  congruent sides
• What other names can a square have?
• quadrilateral
• parallelogram
• rectangle
• rhombus

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Can a rectangle be a square?

• Yes, but not always.
• When?
• Only if all 4 sides are also congruent.

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Can a rhombus be a square?

• Yes, but not always
• When?
• if all 4 angles are right angles.

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Can a trapezoid be a rectangle?

• NO
• Why?
• Trapezoid can have only 1 set of parallel sides.
  Rectangle has 2.

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Is a rectangle always a parallelogram?

• Yes, by its definition.
• a parallelogram with 4 right angles

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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.

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Is a rectangle always a square?

• NO
• Only if the rectangle also has 4 congruent sides.

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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

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Circles

• Almost there

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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

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Radius

• a segment from the center of a circle to a point
  on the circle.
• The plural form of radius is radii.

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Diameter

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

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Chord

• a segment that has both endpoints on the circle.

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Central Angle

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

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Arc

• a part of a circle (along the outside of the
  circle)
• named using just 2 letters

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Semicircle

• a half of a circle.
• named using 3 letters
• Why 3 letters?

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Compass

• a geometric tool used to draw circles and arcs.

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Inscribed Polygon

• a polygon whose sides are chords of a circle.

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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

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A diameter is always chord.

• True or False?
• TRUE!
• by definition, a diameter has two endpoints on
  the circle.

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

• True or False?
• TRUE!
• diameter is equal to the radius times 2.

40
A radius can be a chord.

• True or False?
• FALSE!
• only 1 part of a radius touches the circle, not
  two endpoints.

41
Identify!