High School Geometry Questions

sin 8

AB A 8 BE 6 ED B C DC 2 AC 8 6 4 2 02 4 2 P 4 E D A 6

8 2 d x x2 2 AB BC 8 6 4 2 0 CD 2 B C DE 4 A D EF H E 6 FG 8 GH G F AH P A

46 9ft 4ft perimeter and area of each composite figure Round answers to nearest hundredths 2 15cm 3ft P 6ft 49 A 6 cm P 7cm A 2cm

5 3 1 cm P 3 4 cm A 3 8 cm 3 7 cm 13 in 15 in 5 in 2 in P A

Find the measure of the arc or central angle indicated Assume that lines which appear to be diameters are actual diameters Do not include units in your answer degrees degree symbols etc FR 60

Find the area of each circle Use 3 14 for the value of pi Round your answer 1 poin to the nearest tenth Do NOT include units in your answer ie ft in km etc FR 2 in

Find the area of each Round to the nearest tenth Do not include units in your answer ie ft in km etc triangle FR 3 m 5 9 m

Find the area of each Round to the nearest tenth Do not include units ie ft in km etc square FR 15 8 m 15 8 m 15 8 m 15 8 m

Find the area of each regular polygon Round your answer to the nearest tenth apothem and picture provided FR 9 6 14

Find the area of each parallelogram FR 8 in 18 in

2 1 cm 10 9 cm 12 9 cm 3 1 c a

1 A roll of wrapping paper covers 25 cm Imani plans to wrap the cylinder below in paper a What is the surface area of the cylinder below b How many rolls of paper will Imani need to purchase 4 cm 2 cm

5 Extended Euclid algorithm Does the multiplicative inverse of 59 in Z61 exist If so find it using the extended Euclid algorithm I it does not exist state why Show all your steps

3 Prime factorization a Find the prime factorization of each of these integers Show all your steps 1 108 2 1188 3 10 b Consider two positive integers a 22 x 32 x 52 x 76 and b 24 x 54 x 72 Using the GCD formula not the Euclid algorithm find the greatest common divisor of a and b No need to justifu

Strong Induction Prove the following statement by strong induction There exist non negative integers x y such that n 3x 7y for all n 1

Calculate the lengths of the 2 unlabeled sides JG 6 5 45 G 6 5 H

The given point is reflected across the line indicated Find the coordinates of the image U across x 2 If the given point U is reflected across the line x 2 the image is Type an ordered pair

1 A perimeter and area of each trapezoid Round to nearest tenths Drawings are not to scale 17 in 21 in 16 in 20 in 38 in 2 24 3 cm 8 5cm 9 cm 8 5 cm 9 7 cm 14 4 cm P

for the measure of arc ABC if BD is a diameter the measure of arc DC is 60 degrees and angle DMA is 98 degrees B A M D C

What is the measure of XY N 55 Y

10 Parallelogram FTCV Find FT Find CV x x y y Find FC Find TV P y N 6 02

P 15 2 m 20 m 8 7 2 cm 18 8 m P A 12 5 cm 6 3 cm

3 3 5 m P 4 m A 5 8 m 4 P A 4 7 in 5 7 in 6 in

4 Dana Bill and Rodrigo are given the following information about ATEA m T 71 TA 8 mZE 35 They are asked to determine the number of triangles that can be formed using these conditions and give a reason for their answer Dana says that two triangles are possible because ATEA is an acute triangle Bill says that only one triangle is possible because whenever the measures of two angles and a non included side are given AAS exactly one triangle is possible Rodrigo says that only one triangle is possible because the length of the fixed leg is less than the length of the swinging leg Which of these students is correct Explain

6 7 19 7 cm P 8 m A 12 cm 6 cm X P x 8 cm A

Determine the volume of each of the composite solids below 9 11 4 cm 6 cm 13 cm 5 cm 5 6 cm 6 cm 2 cm 4 in 4 in 6 in 5 in

3 Pre image Quadrilateral HIJK H 2 2 I 2 2 J 2 2 K 2 2 Step 1 Rotate the figure 180 H I J K Step 2 Translate the figure according to x y x 2 y 2 H I I K Step 3 Reflect the figure over the line y x H I J K 3 4

5 r P A 10 cm 7 2 cm 6 18 m 7m X 4cm 8 cm x P A 12m 4 5 m

1 P A x then find the Perimeter and the Area of each triangle Round to nearest tenths Drawings are not to scale x 15 in 12 in 2 6 5 cm x 2 8 cm P A

Find the area of each figure Round to the nearest tenth if necessary Lesson 11 4 18 9 cm 21 cm 19 18 in 12 in 10 in

P A 16ft P A L 9 in

In 3 6 Find the value of each variable drawings are not to scale 3 x 4 x y N 115 99 148 112 176 1329 125 8 49 55 12 20

In 16 Identify all of the terms from the following list that apply to the figure quadrilateral parallelogram rectangle square trapezoid rhombus kite 16 I

15 Kite 1 35 2 34 mzl mz2 12 mz3 mZ4

8 Find the indicated information for the given Kite 3x 5 17 Find x Find y 3y 9

5 x y 115 6 w 122 74 x NO Wo 152 70 81 N

10 Find the indicated information for the given Rhombus EFGH E F GF 30 D Find GD ED 5x 8 EH 34 Find DF Find x H

9 Find the indicated information for the given Isosceles Trapezoid A B D C AC 7x 9 BD 4x 15 Find x Find AC

Find the missing length given the volumes for each figure 1 OC 7 mi 791 68 mi 3 492 81 cm 5 7 184 31 km 6 m 65 97 m

5 Proof by smallest counterexample Prove the following using smallest counterexample 6 n n21 for every positive integer n Note that we will cover proof by strong induction in the number theory homework 00 You got this

2 Pigeonhole principle Prove that if seven distinct numbers are selected from 2 3 4 12 then some two of these numbers will add up to 14 you can assume that the 7 can be picked up more than once Identify the pigeons and the holes Then using the Pigeonhole Principle prove that the statement is true

Use a calculator to evaluate each function Round your answers to four decimal places Be sure the calculator is in the corred angle mode a cos 8 50 29 b sec 56 20

x y z 0 3 2 x 4 2 1 1 x y 2 1 2 Y 2 1 3 x y 2 1 2 Y Z 1 3 3 2x y 2 1 x y 2 5

In 27 Graph the quadrilateral draw its diagonals find the length and slope of each diagonal Then tell whether the diagonals are congruent or not and are they perpendicular or not 27 Square A 5 3 B 5 7 C 9 3 D 1 7 d x x y y2 AC Y2 y m x2 x1 Slope AC Are the diagonals congruent Are the diagonals perpendicular BD Slope BD

11 w y Z 1 0 115 1255

9 w x y 142 65 Z 10 x 152 140 135 76 205 889

hombus 2 3 mZ1 21 Kite mz2 429 m21 mz2 2 mz3 m23 3 46

In 12 17 Find the indicated information for each quadrilateral 12 Parallelogram ABCD B 312 5x 8 y 61 18 D 13 Kite LMNP 3y 6 L Sy 9 X M N 9x 15 12x 3

parallelogram rectangle square trapezoid rhombus kite 26 Identify all of the terms from the following list that apply to each figure quadrilateral 24 H 25 26 H H