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Math AIMS Blitz

This resource covers essential geometric concepts including types of triangles, quadrilaterals, and angles, along with key definitions such as midpoint, perimeter, and bisector. Students will engage with practice problems that involve the use of postulates to prove congruence in triangles, and explore distance and midpoint calculations on the coordinate plane. Definitions for decagons, rhombuses, acute angles, and more are provided, along with various geometry problems and their solutions to effectively reinforce understanding of these mathematical concepts.

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Math AIMS Blitz

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  1. Math AIMS Blitz Geometric Concepts Thursday, March 25 Those interested in taking the on-line test

  2. Period 1 • reflection • isosceles • scalene • equilateral triangle • acute triangle Define or draw. • midpoint • perimeter • bisect • dilation • rotation

  3. Period 1 ANSWERS Define. • midpoint point which cuts a segment in half • perimeter distance around a figure • bisect cut something into half (2 equal parts) • dilation to make smaller or larger • rotation spin • reflectionmirror image • isoscelestwo equal sides • scaleneno equal sides • equilateral triangletriangle with all equal sides (equal angles, too) • acute triangletriangle with all angles less than 90 degrees

  4. Period 2 • decagon • rhombus • acute angle • obtuse angle • right angle Define or draw. • quadrilateral • trapezoid • hexagon • pentagon • octagon

  5. Period 2 ANSWERS Define. • quadrilateral 4-sided polygon (closed shape with straight lines) • trapezoid quadrilateral with only one pair of parallel sides • hexagon 6-sided polygon • pentagon 5-sided polygon • octagon 8-sided polygon 6. decagon 10-sided polygon 7. rhombus quadrilateral with all equal sides • acute angle angle measuring less than 90 degrees • obtuse angle angle measuring more than 90 degrees • right angle angle measuring 90 degrees

  6. Period 3 1. Look at the triangle. 5 4 What is not a possible value of x? x + 2 a. 0 b. 3 c. 5 d. 7 • In the diagram, RT intersects QU at point S. Q Which postulate should be used to prove that T∆RQS  ∆TUS R S a. Side-Side-Side b. Angle-Side-Angle U c. Angle-Side-Side d. Side-Angle-Side 3. In the diagram, MT bisects AH at point T. M Which postulate should be used to prove that ∆MAT  ∆MHT a. Side-Side-Side b. Angle-Side-Angle A T H c. Angle-Side-Side d. Side-Angle-Side

  7. Period 3 x+2 has to be less than 5 + 4 and greater than 5-4 1. Look at the triangle. 5 4 What is not a possible value of x? x + 2 a. 0 b. 3 c. 5 d. 7 • In the diagram, RT intersects QU at point S. Q Which postulate should be used to prove that T∆RQS  ∆TUS R S a. Side-Side-Side b. Angle-Side-Angle U c. Angle-Side-Side d. Side-Angle-Side 3. In the diagram, MT bisects AH at point T. M Which postulate should be used to prove that ∆MAT  ∆MHT a. Side-Side-Side b. Angle-Side-Angle A T H c. Angle-Side-Side d. Side-Angle-Side A S A A S A Mark what is given as A for Angle or S for Side and then compare to answers. S S S S S S

  8. Distance between two points: Midpoint between two points: Period 4 • Points ( 4, 9) and (1, 5) lie on a coordinate plane. What is the distance between the two points? 3. Points ( -1, 5) and (1, -4) lie on a coordinate plane. What is the distance between the two points? 1. The coordinates (2,2) and (-3, 1) are two of the vertices of the figure on the coordinate plane.

  9. Distance between two points: Midpoint between two points: Period 4 ANSWERS • Points ( 4, 9) and (1, 5) lie on a coordinate plane. What is the distance between the two points? 3. Points ( -1, 5) and (1, -4) lie on a coordinate plane. What is the distance between the two points? 1. The coordinates (2,2) and (-3, 1) are two of the vertices of the figure on the coordinate plane.

  10. N Q S M R P • Chords NP and MQ intersect at point S in circle R. If MS = 3, NS = 6, and SQ = 8, what is the length of SP? • a. 9 b. 12 c. 14 d. 4  Period 5 1. Look at circle M. 4 8 What is the value of x? x 6 M a. 4 b. 8 c. 9 d. 12

  11. N Q S M R P • Chords NP and MQ intersect at point S in circle R. If MS = 3, NS = 6, and SQ = 8, what is the length of SP? • 3 x 8 = 6 x what number? • a. 9 b. 12 c. 14 d. 4  Period 5 ANSWERS 1. Look at circle M. 4 8 What is the value of x? x 6 x 8 = 4 x what number? 6 M a. 4 b. 8 c. 9 d. 12

  12. Period 6 2. The area of a larger square is 16 times the area of a smaller square. How many times as long is the base of the larger square than the base of the smaller square? a. 2 times as long b. 4 times as long c. 8 times as longs d. 16 times as long 3. Figure EFGH has a perimeter of 40 cm and an area of 96 cm2. It is dilated by a factor of ¼ to create figure E’F’G’H’. What statement about the perimeter (P) and the area (A) of figure E’F’G’H’ is true? a. P = 10 cm; A = 6 cm2 b. P = 10 cm; A = 24 cm2 c. P = 160 cm; A = 102 cm2 d. P = 160 cm; A = 384 cm2 • How much greater is the volume of a cube when the length of each side is multiplied by 3? a. 3 times as great b. 6 times as great c. 9 times as great d. 27 times as great

  13. Period 6 ANSWERS • How much greater is the volume of a cube when the length of each side is multiplied by 3? Since volume is 3 dimensional, take the amount multiplied by itself 3 times. a. 3 times as great b. 6 times as great c. 9 times as great d. 27 times as great 2. The area of a larger square is 16 times the area of a smaller square. How many times as long is the base of the larger square than the base of the smaller square? Since area is 2 dimensional, find the square root of the area. a. 2 times as long b. 4 times as long c. 8 times as longs d. 16 times as long 3. Figure EFGH has a perimeter of 40 cm and an area of 96 cm2. It is dilated by a factor of ¼ to create figure E’F’G’H’. What statement about the perimeter (P) and the area (A) of figure E’F’G’H’ is true? The factor is ¼… divide the dimensions by 4 and the area (2 dimension) by 42 or 16. a. P = 10 cm; A = 6 cm2 b. P = 10 cm; A = 24 cm2 c. P = 160 cm; A = 102 cm2 d. P = 160 cm; A = 384 cm2

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