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Geometry STAAR Review
Skill 1 - Transversal Lines
Things to remember:
Video 1/State Reporting Category 4
Transversal line – a line that intersects two or more co-planar lines.
• Corresponding Angles are on the same side of a transversal and the same sides of the intersecting lines. They
are congruent if the intersecting lines are parallel.
• Alternate Interior Angles are on opposite sides of a transversal and inside of the intersecting lines. They are
congruent if the intersecting lines are parallel.
• Alternate Exterior Angles are on opposite sides of a transversal and outside of the intersecting lines. They are
congruent if the intersecting lines are parallel.
• Consecutive Interior Angles are on the same side of a transversal and inside of the intersecting lines. They are
supplementary if the intersecting lines are parallel.
Skill 2 - Triangle Properties
Things to remember:
**Triangle Sum THEOREM: The sum of the interior angles of any triangle is always 180°.
• In the Pythagorean Theorem, a2 + b2 = c2, c is always the hypotenuse.
• The rules that work to prove that two triangles are congruent are: SSS, SAS, ASA, SAA, HA, HL
• Remember there is no SSA.
Skill 3 - Nets of 3D Figures
Things to remember:
Net- A flat, 2 dimensional, picture that becomes a 3D shape when folded together. The polygons in the 2D net will
become the faces of the 3D solid.
• Pyramids have triangular lateral faces with 1 base.
• Prisms have rectangular lateral faces with 2 bases. The two bases are congruent polygons.
Skill 4 - Polyhedrons
Things to remember:
Polyhedron- A closed 3 dimensional figure formed by 4 or more polygons that intersect only at their edges. Think: 3D
shape with polygon faces.
• Euler’s Formula: The relationship between the number of vertices, edges, and faces of any polyhedron.
Faces + Vertices = Edges + 2
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)
Skill 6 – Quadrilaterals
Things to remember:
Remember the unique traits that make each quadrilateral specifically.
• Parallelogram: A quadrilateral with opposite sides parallel, opposite sides ≅ , opposite angles ≅ , consecutive
angles supplementary (180°), and both diagonals bisected
B = bh
• Rectangle: A parallelogram with at least 1 right angle, and diagonals ≅ . (4 isosceles Δ’s)
B = bh
• Rhombus: A parallelogram with all sides ≅ , diagonals ⊥ , and diagonals bisect each angle. (4 right Δ’s)
•
•
•
B = ½ d1d2
Square: A parallelogram, Rectangle, and Rhombus combined. No individual traits. (4 right isosceles Δ’s) B = bh
Trapezoid:
B = ½ (b 1 + b 2 )h
Isosceles Trapezoid:
Kite: B = ½ d 1 d 2
Skill 6 Continued
Skill 7 - Circles
Things to remember: 360⁰ in the interior and exterior of a circle
𝐶 = 𝜋𝑑 𝑜𝑟 𝐶 = 2𝜋𝑟
m arc is in degrees
2
𝐴 = 𝜋𝑟
length of arc is a measure arc
• The radius is half of the diameter.
• Angle on circle = ½ arc
• Angle inside = ½(arc + arc)
•
Angle outside = ½(arc - arc)
• Central angle = arc length
• Two chords: (piece)(piece) = (piece)(piece)
• Two secants: (whole)(outside) = (whole)(outside)
• Secant and Tangent: (tangent)² = (whole)(outside)
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐
• Length of arc: AB =
=
• Area of a Sector =
360°
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
360°
=
2𝜋𝑟
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟
𝜋𝑟²
Skill 8 - Probability
Things to remember:
Chance of success
All possible outcomes
X 100
Skill 9 - Composite Figures
Things to remember:
• Composite tells you to add or subtract the shapes (Volume or Area)
• Write the formulas down before you work.
Composite Figures 2 dimensional - A plane figure made up of triangles, rectangles, trapezoids, circles, and other simple
shapes.
Composite Figures 3 dimensional - A 3-D figure made up of pyramids, prisms, cylinders, cones, spheres, or hemispheres.