SUPPLEMENTARY ANGLES

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# SUPPLEMENTARY ANGLES - PowerPoint PPT Presentation

SUPPLEMENTARY ANGLES. 2-angles that add up to 180 degrees. COMPLEMENTARY ANGLES. 2-angles that add up to 90 degrees. Vertical Angles . Vertical Angles are Congruent to each other. <1 =<3 <2=<4 <1+<2=180 degrees <2+<3=180 degrees <3+<4=180 degrees <4+<1=180 degrees.

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## PowerPoint Slideshow about 'SUPPLEMENTARY ANGLES' - yitta

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Presentation Transcript

### Vertical Angles

Vertical Angles are Congruent to each other
• <1 =<3
• <2=<4
• <1+<2=180 degrees
• <2+<3=180 degrees
• <3+<4=180 degrees
• <4+<1=180 degrees

### The sum of 2-sides of a triangles must be larger than the 3rd side.

(Upside down T!!!!)

(Big Angle Small Angle!!!!!)

CENTROID

MEDIANS ARE IN A RATIO OF 2:1

### Properties of a Parallelogram

Parallelogram
• Opposite sides are congruent.
• Opposite sides are parallel.
• Opposite angles are congruent.
• Diagonals bisect each other.
• Consecutive (adjacent) angles are supplementary (+ 180 degrees).
• Sum of the interior angles is 360 degrees.

### Properties of a Rectangle

Rectangle
• All properties of a parallelogram.
• All angles are 90 degrees.
• Diagonals are congruent.

### Properties of a Rhombus

Rhombus
• All properties of a parallelogram.
• Diagonals are perpendicular (form right angles).
• Diagonals bisect the angles.

### Properties of a Square

Square
• All properties of a parallelogram.
• All properties of a rectangle.
• All properties of a rhombus.

### Properties of an Isosceles Trapezoid

Isosceles Trapezoid
• Diagonals are congruent.
• Opposite angles are supplementary + 180 degrees.
• Legs are congruent

### PROVE A PARALLELOGRAM

Prove a Parallelogram
• Distance formula 4 times to show opposite sides congruent.
• Slope 4 times to show opposite sides parallel (equal slopes)
• Midpoint 2 times of the diagonals to show that they share the same midpoint which means that the diagonals bisect each other.

### How to prove a Rectangle

Prove a Rectangle
• Prove the rectangle a parallelogram.
• Slope 4 times, showing opposite sides are parallel and consecutive (adjacent) sides have opposite reciprocal slopes thus, are perpendicular to each other forming right angles.

### How to prove a Square

Prove a Square
• Prove the square a parallelogram.
• Slope formula 4 times and distance formula 2 times of consecutive sides.

### Prove a Trapezoid

Prove a Trapezoid
• Slope 4 times showing bases are parallel (same slope) and legs are not parallel.

### Prove an Isosceles Trapezoid

Prove an Isosceles Trapezoid
• Slope 4 times showing bases are parallel (same slopes) and legs are not parallel.
• Distance 2 times showing legs have the same length.

### Prove Isosceles Right Triangle

Prove Isosceles Right Triangle
• Slope 2 times showing opposite reciprocal slopes (perpendicular lines that form right angles) and Distance 2 times showing legs are congruent.
• Or Distance 3 times and plugging them into the Pythagorean Theorem

### Prove an Isosceles Triangle

Prove an Isosceles Triangle
• Distance 2 times to show legs are congruent.

### Prove a Right Triangle

Prove a Right Triangle
• Slope 2 times to show opposite reciprocal slopes (perpendicular lines form right angles).

### Measure of one Exterior Angle

The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points.

### 2-intersecting lines that bisect the angles that are formed by the intersecting lines

Isometry: Transformation that Preserves Distance
• Dilation is NOT an Isometry
• Direct Isometries
• Indirect Isometries
Direct Isometry
• Preserves Distance and Orientation (the way the vertices are read stays the same)
• Translation
• Rotation
Opposite Isometry
• Distance is preserved
• Orientation changes (the way the vertices are read changes)
• Reflection
• Glide Reflection

CENTRAL ANGLE

m∠O = m arc-AB

A

o

B