High School Geometry Questions

n 16 19 Find the value of each variable Answers should be in simplest radical form 5 17 45 X 459 14 X 45 24 45

n 6 7 Rationalize the denominator answer in simplest radical form 3 5 7 6 14

12 List the sides for the triangle in order from shortest to longest drawing is not to scale D 56 The lengths for the sides of a frin 13 List the angles for the triangle in order from smallest to greatest drawing is not to scale 5 9 in 8 2 in 5 2 in B

4 5 2 5 9 5 5 18 8

n 1 5 Completely simplify each radical expression 500 2 6 75 GEOMETRY Unit 7 Te

2 Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU 7 A Rotate GHJ using center G until GH is lined up with ST and then reflect over aline halfway between GHJ and STU B Translate GHJ by the directed line segment GS Rotate GHJ using S as the center by angle H ST Reflect G HJ over ST NAME C Translate GHJ by the directed line segment GT Rotate GHJ using Tas the center by angle HTS Reflect G HJ over ST D Translate GHJ by the directed line segment GS Translate G H J by the directed line segment HT Translate G HJ by the directed line segment T 3 Reflect triangle STU across line ST Which of these is a valid reason why the image of U will coincide with J A The image of U and J are on the same side of ST and make the same angle with it at T B The image of U and Jare the same distance along the same ray from T C The image of U and I will not coincide after reflection over ST 2019 by Illustrative Mathematics D Line ST is the perpendicular bisector of the segment connecting U and J because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment 4 Here is parallelogram ABCD U DATE M B illustrative Mathematics PERIOD 2

TRIG 34 A blue bird sitting in its nest at the top of a tree spots a large red apple in Donovan s hands at an angle of depression of 23 If the nest is 20 ft off the ground and the apple is 4 ft off the ground how far is Donovan from the tree Be sure to draw an appropriate diagram

ric Summary 3 points 1 m2CAB 1 m2DAB 1 conclusion reasoning A h 5 14 0 B 0 Cos123 53 13 A 4 in 3 O 10 B 3 d a Your friend gives you the right triangle above and to the left and says Bisecting an angle is really easy Take triangle ABC If I wanted to bisect ZCAB all I need to do is find the midpoint of BC The ray that goes from A through the midpoint of BC will cut ZCAB in half because it cuts the side BC in half Your friend then sketches the triangle above and to the right so that point D is the midpoint of side BC Convince your friend that they are wrong Use trigonometry to show that ZDAB and CAD are not congruent Show all work Use complete sentences to explain your conclusion and reasoning

Find the value of each variable answers should be in simplest radical form 1 45 y X 2 2 U V 30 3 45 6

4 X 16 60 y 5 U V 45 8 2 6 a 3 b 60

Rotations of Shapes Date Graph the image of the figure using the transformation given List the new vertices 1 rotation 180 about the origin H M Las Ay 3 rotation 90 clockwise about the origin Ay H HY 5 rotation 90 clockwise about the origin U 1 2 w 0 2 K 3 2 G 3 3 Ay x Name 7 rotation 180 about the origin z 1 5 K 1 0 C 1 1 N 3 2 9 rotation 90 clockwise about the origin 2 rotation 90 counterclockwise about the origin 4 rotation 180 about the origin Ay 6 rotation 180 about the origin v 2 0 S 1 3 G 5 0 Ay x Find the coordinates of the vertices of each figure after the given transformation List the new Vertices 8 rotation 180 about the origin L 1 3 Z 5 5 F 4 2 Period 10 rotation 180 about the origin OVER

Find the value of each variable Answers should be in simplest radical form 26 27 8 45 y X 450 21 60 X 30 28 450 12 y 459 X

21 A 6 8 cm B The les List the angles for each triangle in order from smallest to greatest drawings are not to scale 22 K 8 2 cm 6 1 cm C 10 9 in 9 8 in L N 10 2 in

29 30 V 60 30 45 X y 45 6 31 60 16 30

7 5 3 9 3 8 10 5 5 4 7 9 18 4 2

The lengths for the sides of a triangle are given Classify each triangle as acute right or obtuse 23 110 100 20 25 10 6 9 24 25 24 7

16 10 in 6 in 17 in 17 2 5 ft 24 ft X 18 4 m 3 6 m 12 m

4 7 14 5 4 5 6 10 6

19 A 19 20 List the sides for each triangle in order from shortest to longest drawings are not to scale 20 L B 52 In 21 22 L 489 M 1130 34

tionalize each denominator answer in simplest radical form 5 12 11 6 3 12

Completely simplify each radical expression 1 63 2 112

5 Find the value of x that makes ALMN APQR L 10 M 12 R X 7 N 6 Q 5 P

Find the value of x that makes AABC AADE helmi2 elgnan Ad qclav nguons zi noto 28 WO A 30 E B 10 1

X Y 2 y 3 2 x 1 1 3 33

6 1 point The pentagon shown could be reflected over which line to be carried onto itself x axis y axis line y x not possible

5 1 point If the pentagon below is to be reflected over the y axis which point would not move at all L K 1 Point H Point J Point K Point G 1 G H 3 1

2 Point Slope Form 1 3 Graph the line that represents each linear equation 1 y2 2 x 3 2 y 3 2 x 1 P 5 1 3 y 1 x 5 2

Problem 1 Part A Find the area of the shape below All measurements are in meters A 6 LC Do not include units square meters in your answer Type your answer below as a number example 5 3 1 41 2 or 3 2 Part B Find the area of the shape below All measurements are in meters 5 4 33 7

A scale model of an oil tanker truck can hold 1 gallon of oil If a trucking company wants the full size truck to hold 8 000 gallons of oil what scale factor must they apply to the mode