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Geometry STAAR Review
Video 4/State Reporting Category 2
Skill 1- Triangle Similarity
Things to remember:
What makes shapes similar? Angles congruent and sides proportional
AA~
SAS~: (Included angle)
SSS~
If you see a triangle in another triangle, draw each triangle separately and label what you know
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•
•
•
N
L
2
M
1
O
x+1
<
1
N
x
<
U
9
L
P
8
M
T
NP = _______
Similar: yes or no
LN = _______
Justify: ______________
6
S
Skill 2- Right Triangles
Things to remember:
• The triangle has two legs that form the right angle and a hypotenuse that is across from
the right angle.
• Pythagorean Theorem: a2 + b2 = c2
• Special Right Triangles:
30⁰ – 60⁰ – 90⁰: x, x 3 , 2x
45⁰ - 45⁰ - 90⁰: x, x, x 2
• Can be used to find distance
Skill 3- Parallelograms
Things to remember:
• 5 Properties of Parallelograms:
1. two sets of opposite sides are parallel
2. two sets of opposite sides are congruent
3. two sets of opposite angles are congruent
4. consecutive angles are supplementary
5. diagonals bisect each other
• Parallelograms
P = ℓ + w + ℓ + w or b + h + b + h
B = ℓw or bh
• Rectangles
• P = ℓ + w + ℓ + w or b + h + b + h
• B = ℓw or bh
• Rhombus
P = 4s
B = 1 d1d2
2
• Square
P = 4s
B = s2
Skill 4 - Polygons
Things to remember:
• N – gon: general form
• Polygons with names:
Name
Number of Sides
Triangle
3
Quadrilateral 4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
n-gon
n
Number of Angles
3
4
5
6
7
8
9
10
11
12
n
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•
Regular – all sides are congruent and all angles are congruent
Irregular – no side is necessarily congruent and no angle is necessarily congruent
Convex – all the angles are pushing out of the shape
Concave - at least one of the angles is caving in to the shape
B = 1 Pa ( Special Right Triangle Rules may apply here)
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Apothem (a) – the distance from the center of the polygon to the midpoint of a side
Radius – the distance from the center of the polygon to a vertex
Sum of the interior angles: 180°(n − 2)
Measure of each interior angle: 180°(n − 2)
2
n
• Sum of the exterior angles for all polygons: 360⁰
• Measure of each exterior angle: 360°
n
Skill 5- Transformations
Things to remember:
• Reflection across the x-axis: (x, y) → (x, -y)
• Reflection across the y-axis: (x, y) → (-x, y)
• Reflection across the line y = x: (x, y) → (y, x)
• Rotations: clockwise and counter-clockwise
Order – how many times you rotate a picture and it looks exactly the same.
Angle of Rotation -
360⁰
𝑜𝑟𝑑𝑒𝑟
• Translation: (x + a, y + b) or (x – a, y – b)
• Dilation when centered at the origin: (kx, ky) k is scale factor
𝒌(𝑟𝑖𝑠𝑒)
• Dilation not centered at the origin:
𝒌(𝑟𝑢𝑛)