mcas review geometry and measurement. circle formulas circumference is the distance around a circle....
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MCAS REVIEW GEOMETRY AND MEASUREMENT
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CIRCLE FORMULAS
Circumference is the distance around a circle.
Both the circumference and area formula require you to find the radius!
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CIRCLE - PRACTICE
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PYTHAGOREAN THEOREM Got a right triangle? Need to find a missing side? The Pythagorean Theorem is here to save the day! It is NOT on the MCAS Reference Sheet. You will need to remember it on the day of the test!
Remember: The hypotenuse is the side across from the right angle (“the box”).
Strategy: You can also use it to find the distance between 2 points.
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PYTHAGOREAN THEOREM-PRACTICE
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SPECIAL RIGHT TRIANGLES#5
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SIMILAR FIGURES
The Facts: 1. Corresponding angles are CONGRUENT.2. Corresponding sides are PROPORTIONAL.
Strategy: If given a similarity statement, connect the corresponding angles.
For example: .
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CONGRUENT FIGURES
The Facts: 1.Corresponding angles
are CONGRUENT.2.Corresponding sides are
CONGRUENT.
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LATERAL SURFACE AREA FORMULAS
Lateral area is the total area of all the surfaces that a figure has but DOES NOT include the bases of the figure.
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LATERAL SURFACE AREA-PRACTICE
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TOTAL SURFACE AREA FORMULAS
Is the sum of the areas of ALL the surfaces that a figure has.
Examples: Wrapping PaperOrange
TIP: You have most of the formulas at your fingertips to solve total surface area problems. If you don’t have the formula for a given figure, just find the area of each side and add them up!
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TOTAL SURFACE AREA - PRACTICE
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VOLUME FORMULASIs the amount of 3D space an object occupies. Its units are always “cubic”.
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VOLUME FORMULAS#14
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ReflectionTranslation
TRANSFORMATIONS
Rotation Dilation
A reflection produces a mirror image of a figure along a line of reflection.
A translation moves every point on a figure the same distance in the same direction.
A rotation turns a shape about a fixed point. To perform a rotation, three details are needed: 1) The center 2) The angle of rotation and 3) The direction of rotation
A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape.
A dilation is a transformation that produces an image that is the same shape as the original, but a different size. A dilation stretches or shrinks the original figure.
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TRANSFORMATIONS-PRACTICE
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PARALLEL LINES CUT BY A TRANSVERSALWhen two parallel lines are cut by a transversal, sets and pairs of specific angles are created. Some of these angles have special characteristics:
Corresponding - Congruent
Alternate Interior - Congruent
Alternate Exterior - Congruent
Vertical Angles (“X”) - Congruent
Same Side Interior –Supplementary
Interior
Exterior
Exterior
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PARALLEL LINES CUT BY TRANSVERSAL-PRACTICE
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PERIMETER
Perimeter is the distance around a shape. Add up ALL the sides!TIP: Make sure you LABEL all the sides before you add them!
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AREA FORMULAS
Is the amount of space inside a 2D shape. It is the number of unit squares that can be contained within it.
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AREA FORMULAS-PRACTICE #26
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ARITHMETIC VS. GEOMETRIC SEQUENCES
An arithmetic sequence of numbers where the difference between the consecutive terms in constant. Each term in the sequence is generated by adding the same value to the previous term.
A geometric sequence is a sequence of numbers where there is a constant ratio between the consecutive terms. Each term in the sequence is generated by multiplying each previous term by the same value.
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ARITHMETIC VS. GEOMETRIC SEQUENCES
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ANSWER KEY 1.) C
2.) B
3.) B
4.) C
5a.) 6 miles
5b.) 10.4 miles
5c.) Nancy 6.9 miles
Sanjiv 12 miles
12-6.9=5.1 miles
6.) A
7.)
8.) C
9.) 320 square centimeters10.) A11.)D12.) B13.)C14.) C15.) B16.) B17.) A18.) C19.) D20.) A21.) B22.)C
23.) B24.) C25.) 48 square centimeters26.) C27.) C28.) D29.) C30.) C31.) D32.) A33.) C