Station 1 – Pythagorean Theorem

Solve for x. Round to the nearest tenth or simplest radical form. 1. 2.

3. An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer if they swim from one corner to the opposite? 4. A 20-foot ramp is used at the loading dock of a factory. If the base of the ramp is placed 19 feet from the base of the dock, how high is the loading dock?

Station 2 – SOH-CAH-TOA

1. Find each trigonometric ratio. Give your answer as a fraction in simplest form. 2. Solve for x. Round your answer to the nearest tenth. a. b. c. **3. Find the height of the tree.

Station 3 – Special Right Triangles

Find the value of each variable. 1. 2.

3.

Station 4 – Applications of Elevation and Depression

Use a picture to help solve the problem. Round your answer to the nearest tenth. 1. The town park does an outdoor movie night every Saturday during the summer on a large screen. Kate is sitting 36 feet from the base of the screen, watching a movie with her family. If the angle of elevation from Kate to the top of the screen is 24°, how tall is the movie screen? 2. While parasailing, Ryan spots a dolphin on the water below. If Ryan is 228 feet above the water and the angle of depression is 15°, what is the horizontal distance between Ryan and the dolphin?

Station 5 – Midsegments

1. Point M, N, and P are the midpoints of the sides of QRS.

QR = 35, MP = 24, and SP = 14 Find the length of: NP = RS = SQ = MN = 2. Solve for x. 3. Which distance is shorter, kayaking from A to B to C or walking from A to X to C?

Station 6 – Triangles

1. Solve for x. 2. Find the measure of each angle. a. <1 = b. <2 = c. <3 = d. <4 = e. <5 = f. <6 = 3. Do the following side lengths form a triangle, and if so, what type?

a. 12, 13, 18 b. 4, 5, 9 c. 7, 8, 10

Station 7 – Transformations (Translations)

1. Describe the translation from the pre-image to the image.

2. Write the new ordered pairs after the following translation T(-2, 1).

A(2, -4), B(-2, 6), C(9, 7)

3. The point M(10, 3) has been translated under the rule (x – 3, y + 5), what is the

ordered pair of the pre-image point M.

4. Given B’(-3, 4) and B(5, -3), write the translation rule that was used.

Station 8 – Transformations (Rotations)

1. What will be the new position of the given point (1, -9) after rotating 90

counterclockwise about the origin?

2. Write the rule of the transformation below.

3. List the new ordered pairs after a rotation of 180 about the origin.

M(0, 5), A(-2, -3), T(1, 10), H(-4, 5)

Station 9 – Transformations (Reflections)

1. List the new ordered pairs after a reflection over the x-axis.

2. Using the following points, identify the new ordered pairs after a reflection over the line

y = x.

A(-7, 9), B(0, 14), C(11, -5)

3. Find the coordinates of the vertices of each figure after the given transformations.

Reflection across y = -3

Station 10 – Dilations

1. List the new coordinates of rectangle PQRS after a dilation with a scale factor of ¼,

centered at the origin.

2. On the graph below, point A is the center of dilation. If the line segment is dilated by a

scale factor of 2 with A being the center, list the new coordinates of B and C after the

dilation.

Station 11 – Midpoint & Distance Formula

1. On a map’s coordinate grid, Walt City is located at (-1, -3) and Koshville is located at

(4, 9). How long is the train’s route as the train travels along a straight line from Walt City

to Koshville?

2. What is the midpoint between Walt City and Koshville?

3. Find the perimeter of the triangle below.

Station 12 – Triangle Congruence

Determine whether the triangles are congruent. If so, state how. (SSS, SAS, ASA, HL,

AAS)

1. 2. 3.

4. 5.

6. If 2 angles and the non-included side of 1 triangle are congruent to 2 angles and the

non-included side of another triangle, the two triangles are congruent by which postulate?

7. If 2 angles and the included side of 1 triangle are congruent to 2 angles and the

included side of another triangle, the two triangles are congruent by which postulate?

Station 13 – Proofs

1. Given: 𝑆𝑄̅̅̅̅ and 𝑃𝑅̅̅ ̅̅ bisect each other

Prove: RST PQT

Statements Reasons

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

2. Given: <B <E, 𝐴𝐵̅̅ ̅̅ 𝐷𝐸̅̅ ̅̅ , C is the midpoint of 𝐵𝐸̅̅ ̅̅

Prove: <A <D

Statements Reasons

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

Station 14 – Transversals

Use the picture for questions 1 and 2, solve for x.

1. m<1 = 3x – 17, m<2 = x + 1

2. m<3 = 20k + 11, m<4 = 8k + 1

3. Find the value of x and y.

Station 15 – Similarity

1. If TSR ~ TNM, find the length of x.

2. Using similar triangles, find the height of the tree.

**3. A 5-foot person standing 20 feet from a tree casts a 6-ft shadow. What is the height

of the tree?