GEOMETRY AND MEASUREMENT Mcas REVIEW GEOMETRY AND MEASUREMENT

Circle formulas Circumference is the distance around a circle. Both the circumference and area formula require you to find the radius!

Circle - practice #1

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.

Pythagorean theorem-Practice #4 #3 #2

Special right triangles #5

Similar figures~ #6 The Facts: Corresponding angles are CONGRUENT. Corresponding sides are PROPORTIONAL. Strategy: If given a similarity statement, connect the corresponding angles. For example: 𝐴𝐵𝐶~𝐷𝐸𝐹.

Congruent figures ≅ #7 The Facts: Corresponding angles are CONGRUENT. Corresponding sides are CONGRUENT.

Lateral Surface area formulas #8 Lateral area is the total area of all the surfaces that a figure has but DOES NOT include the bases of the figure.

Lateral surface area-Practice #10 #9

Total surface area formulas Is the sum of the areas of ALL the surfaces that a figure has. 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! Examples: Wrapping Paper Orange

Total surface area - practice #12 #11

Volume formulas #13 Is the amount of 3D space an object occupies. Its units are always “cubic”.

Volume formulas #15 #16 #14

Translation Reflection TRANSFORMATIONS Rotation Dilation A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. Translation Reflection 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. TRANSFORMATIONS 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 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. Rotation Dilation

Transformations-practice #19 #18 #17

Parallel lines cut by a transversal When 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 Exterior Interior Exterior

Parallel lines cut by transversal-practice #21 #22 #20

Perimeter #23 #24 Perimeter is the distance around a shape. Add up ALL the sides! TIP: Make sure you LABEL all the sides before you add them!

Area formulas #25 Is the amount of space inside a 2D shape. It is the number of unit squares that can be contained within it.

Area formulas-Practice #29 #26 #27 #28

Arithmetic vs. geometric sequences #30 #31 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.

Arithmetic vs. geometric sequences #33 #32

Answer key 9.) 320 square centimeters 10.) A 23.) B 11.)D 24.) 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.) 𝑚∠𝑁=64° 8.) C 23.) B 24.) C 25.) 48 square centimeters 26.) C 27.) C 28.) D 29.) C 30.) C 31.) D 32.) A 33.) C