1. RIGHT TRIANGLES A² + B² = C² C
“SIDE A AND SIDE B ALWAYS MEET AT THE RIGHT ANGLE” C A B

2. SPECIAL RIGHT TRIANGLES
45 ° -45 ° -90 °
30 ° -60 ° -90 °

3. 30 °- 60 °- 90° TRIANGLES
THESE SPECIAL RIGHT TRIANGLES HAVE A 90 ° ANGLE, AND MUST HAVE A 30 ° ANGLE AND A 60 ° ANGLE.
THE SIDE DIRECTLY ACROSS THE 30 ° ANGLE MEASURES X.
THE SIDE DIRECTLY ACROSS THE 60 ° ANGLE MEASURES X(SQRT 3).
THE SIDE DIRECTLY ACROSS THE 90 ° ANGLE MEASURES 2X.

4. 30°- 60°- 90° TRIANGLES 60 °→ X(SQRT 3) 90 °→ 2X 30° → X 30 ° 2X

5. 45 ° - 45 ° - 90 ° TRIANGLES
THESE SPECIAL RIGHT TRIANGLES HAVE A 90 ° ANGLE, AND MUST HAVE TWO 45 ° ANGLES.
THE SIDES DIRECTLY ACROSS THE 45° ANGLES EACH MEASURE X.
THE SIDE DIRECTLY ACROSS THE 90 ° ANGLE MEASURES X (SQRT 2).

6. 45° - 45 ° - 90 ° TRIANGLES 45 °→ X 90 ° → X(SQRT 2) 45° X (SQRT 2) X

7. REMINDER: ANGLES OF A TRIANGLE
the sum of the three angles of any triangle add up to 180 °
x ° + y °+z °= 180 °
x °
z °
y °

8. The drawing to the right shows 3 square parking lots that enclose a grassy area shaped like a right triangle.
If Lot A’s perimeter is 300 yards and lot B’s perimeter is 400 yards, what is the perimeter of Lot C?
A 500 yd
B 700 yd
C yd
D yd
Problem #6
Obj 7 - TAKS th [8.7(C)]

9. Look at the right triangle shown to the right
Look at the right triangle shown to the right. Which of the following could be the triangle’s dimensions?
A 12, 16.8, 18.2
B 5.4, 10.6, 16
C 1.2, 1.6, 2
D 8, 10, 12.5
Problem #9
Obj 7 - TAKS th [8.7(C)]

10. Which figure best represents a triangle with sides a, b, and c in which the relationship a2 + b2 = c2 is always true?
Problem #21
Obj 7 - TAKS th [8.7(C)]

11. What is the area of the largest square in the diagram? A. 5 units2
B. 9 units2
C. 16 units2
D. 25 units2
Problem #24
Obj 7 - TAKS th {8.7(C)]

12. The sides of squares can be used to form triangles
The sides of squares can be used to form triangles. The areas of the squares that form right triangles have a special relationship.
Problem #29
Obj 7 - TAKS th [8.7(C)]

13. Using the dimensions of the squares shown below screen, determine which set of squares will form a right triangle.
Problem #29
Obj 7 - TAKS th [8.7(C)]

14. A fence around a square garden has a perimeter of 48 feet
A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden.
A. 12 feet
B. 17 feet
C. 21 feet
D. 24 feet
Problem #33
Obj 6 - TAKS th [G.C1(C)]

15. Use the Pythagorean theorem to find the figure that is a right triangle.
A. C.
B. D.
Problem #31
Obj 7 - TAKS th [8.7(C)]

16. A slide was installed at the local swimming pool, as shown below.
Which is closest to the length of the slide?
A. 29 ft
B. 16 ft
C. 21 ft
D. 81 ft
Problem #53
Obj 8 - TAKS th 8.9(A)]

17. Mr. Carpenter built a wooden gate, as shown below.
Which is closest to the length in feet of the diagonal board that Mr. Carpenter used to brace the wooden gate?
A. 4.9 ft
B. 5.3 ft
C. 6.1 ft
D. 6.9 ft
Problem #46
Obj 8 - TAKS th 8.9(A)]

18. The drawing shows part of the plan for a new underground lawn-sprinkler system.
Which is closest to the length of the section of plastic pipe from point A to point C?
A. 4.7 ft
B. 5.7 ft
C. 6.7 ft
D. 7.7 ft
Problem #32
Obj 8 - TAKS th [8.9(A)]

19. The total area of trapezoid FGHJ is 52 square inches.
What is the approximate length of segment FJ?
A. 8.0 inches
B. 8.5 inches
C inches
D inches
Problem #41
Obj 8 - TAKS th G.E1(C)]

20. In a town there is a small garden shaped like a triangle, as shown to the right. The side of the garden that faces Sixth Street is 80 feet in length. The side of the garden that faces Third Avenue is 30 feet in length.
What is the approximate length of the side of the garden that faces Elm Street?
A. 35 ft
B. 40 ft
C. 85 ft
D. 110 ft
Problem #31
Obj 8 - TAKS th [8.9(A)]

21. Which expression could be used to determine how far Kim walked?
Kim walked diagonally across a rectangular field that measured 100 feet by 240 feet.
Which expression could be used to determine how far Kim walked? A B C D
Problem #24
Obj 8 - TAKS th [G.E1(C)]

22. Mrs. Cheung hired a landscaping service to plant a row of bushes around her triangular backyard.
If the bushes must be planted 3 feet apart, approximately how many bushes are needed for Mrs. Cheung’s backyard?
A 23
B 25
C 28
D 32
Problem #16
Obj 8 - TAKS th [8.9(A)]

23. A square park has a diagonal walkway from 1 corner to another
A square park has a diagonal walkway from 1 corner to another. If the walkway is about 38 yards long, what is the approximate length of each side of the park?
A 6 yd
B 19 yd
C 27 yd
D 54 yd
Problem #12
Obj 8 - TAKS th [8.9(A)]

24. A cell-phone tower that has a transmission range of 50 miles is located 40 miles due south of a straight road.
Find x, the length of the section of road that is within the transmission range of the tower.
A. 10 mi
B. 30 mi
C. 60 mi
D. 90 mi
Problem #6
Obj 8 - TAKS th [8.9(A)]

25. Which is closest to the length of the walkway?
Mr. Elliott designed a flower garden in the shape of a square. He plans to build a walkway through the garden, as show to the right.
Which is closest to the length of the walkway?
A 36 ft
B 24 ft
C 17 ft
D 13 ft
Problem #1
Obj 8 - TAKS th [8.9(A)]

26. What are the measures of the three angles of the garden?
On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island by the intersections of four streets shown.
What are the measures of the three angles of the garden?
A. 90°, 65°, 25°
B. 90°, 50°, 40°
C. 90°, 60°, 30°
D. 130°, 40°, 10°
Problem #32
Obj 6 - TAKS th [G.C1(A)]

27. Look at the drawing shown to the right.
If KMP is a right triangle formed
by the placement of 3 squares,
what is the area of the shaded square?
A in.2
B. 24 in.2
C. 66 in.2
D. 81 in.2
Problem #41
Obj 7 - TAKS th [8.7(C)]

28. If the perimeter of this trapezoid is 32 units, what is its area?
The lengths of the bases of an isosceles trapezoid are shown to the right.
If the perimeter of this trapezoid is 32 units, what is its area?
A 44 square units
B 110 square units
C 88 square units
D 55 square units
Problem #15
Obj 6 - TAKS th [G.C1(C)]

29. The drawing below shows how 3 squares can be joined at their
vertices to form a right triangle.
Which is closest to the area in square inches of the largest square?
A in.2
B in.2
C in.2
D in.2
Problem #46
Obj 7 - TAKS th [8.7(C)]

30. The drawing to the right shows 3 square parking lots that enclose a grassy area shaped like a right triangle.
If Lot A’s perimeter is 300 yards and lot B’s perimeter is 400 yards, what is the perimeter of Lot C?
A 500 yd
B 700 yd
C yd
D yd
Problem #6
Obj 7 - TAKS th [8.7(C)]

31. Look at the right triangle shown to the right
Look at the right triangle shown to the right. Which of the following could be the triangle’s dimensions?
A 12, 16.8, 18.2
B 5.4, 10.6, 16
C 1.2, 1.6, 2
D 8, 10, 12.5
Problem #9
Obj 7 - TAKS th [8.7(C)]

32. How tall was the part of the pole that was left standing?
A wooden pole was broken during a windstorm. Before it broke, the total height of the pole above the ground was 25 feet. After it broke, the top of the pole touched the ground 15 feet from the base.
How tall was the part of the pole that was left standing?
A 8 ft
B 10 ft
C 17 ft
D 20 ft
Problem #21
Obj 10 - TAKS th [8.14(B)]

33. Mrs. Aman asked her students to look at the drawing
shown below to determine the length of d.
Which of the following student responses best represents
the length of d?
A. 8 units
B. 11 units
C. 14 units
D. 3 units
Problem #89
Obj 10 - TAKS th [8.15(A)]

34. Which is closest to the length of the hose in the garden? A. 7.8 ft
Mr. Schultz has a garden shaped like an equilateral triangle that measures
11 feet on each side. He has placed a watering hose that extends from the faucet located at a vertex to the opposite side, as shown below.
Which is closest to the length of the hose in the garden?
A ft
B ft
C ft
D ft
Problem #49
Obj 6 - TAKS th [G.C1(C)]

35. WY is 10 centimeters long. Find the length of XZ. F. 5 cm G. 10 cm
WXY is isosceles.
WY is 10 centimeters long. Find the length of XZ.
F cm
G cm
H cm
J cm
Problem #54
Obj 8 - TAKS th G.E1(C)]

36. About how high off the ground is kite? A 110 ft B 127 ft C 156 ft
A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground.
About how high off the ground is kite?
A 110 ft
B 127 ft
C 156 ft
D 311 ft
Problem #12
Obj 6 - TAKS th [G.C1(C)]

37. Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet
Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet. He sees a cornfield at an angle of depression of 30°.
What is Mr. Ryan’s approximate horizontal distance from the cornfield at this point?
A feet
B feet
C feet
D feet
Problem #36
Obj 6 - TAKS th [G.C1(C)]

38. Look at the cube shown below.
Which equation best represents the area of the shaded rectangle located diagonally in the cube?
A. A = C. A =
B. A = D. A =
Problem #50
Obj 6 - TAKS th [G.B4(A)]

39. In the figure shown below, MN = 10 centimeters.
Which is closest to the length of TN?
A. 7 cm
B. 6 cm
C. 17 cm
D. 14 cm
Problem #54
Obj 6 - TAKS th [G.C1(C)]