Congruent
Figures
Similar
Figures
Triangle
Trigonometry
Surface area and Volume
Probability
100

Are two squares with the same size congruent?


Yes, they are congruent because they have the same shape and size.

100

Triangle A has sides 6 cm, 8 cm, and 10 cm.

Triangle B has its shortest side equal to 9 cm.

What are the lengths of the other two sides of Triangle B?

The other sides are 12cm and 15 cm

100

In triangle ABC, angle A = 30°, and the side opposite angle A (BC) = 10 cm. Find the hypotenuse (AC) assuming it’s a right triangle at B.


Area formula:

\text{Area} = \frac{1}{2}ab\sin(C)


= \frac{1}{2}(8)(6)\sin(45°) = 24 \times 0.7071 \approx 16.97 \text{ cm}^2


100

Find the volume of a sphere with radius 7 cm

Calculation:


=(4/3) × 3.14×73

100

A point is chosen at random inside a square of side length 4 units. What is the probability that it lands inside a circle of radius 2 units inscribed in the square?



  • Area of square: 4 \times 4 = 16
  • Area of circle: \pi \times 2^2 = 4\pi
  • Probability:
    P = \frac{4\pi}{16} = \frac{\pi}{4}


200

Rectangle A has a length of 6 cm and a width of 3 cm.

Rectangle B has a length of 6 cm and a width of 3 cm.

Are the two rectangles congruent?

Yes, the rectangles are congruent because they have the same shape and exact same side lengths.

200

A map uses a scale where 1 inch

Two towns are 3 inches apart on the map.

How many miles apart are the towns in real life?

The towns are 15miles apart

200

In a right triangle, one of the acute angles is 35°, and the hypotenuse is 12 cm. Find the length of the side opposite the 35° angle.



Answer: The opposite side is approximately 6.89 cm long.


200

A cone has a radius of 3 cm and a height of 9 cm

Find its volume

(Use TT = 3.14)

=(1/3) x3.14x32x9

200

A point is randomly selected inside a triangle with area 20 square units. Inside the triangle is a smaller triangle with area 5 square units.

What is the probability that the point lands inside the smaller triangle?


Solution:


P = \frac{\text{Area of smaller triangle}}{\text{Area of larger triangle}} = \frac{5}{20} = \boxed{\frac{1}{4}}


300

Are these two triangles congruent?


Triangle A has sides 3 cm, 4 cm, and 5 cm.

Triangle B has sides 3 cm, 4 cm, and 5 cm.


Yes, the two triangles are congruent because all three sides are the same length.

300

A side of the smaller polygon is 8 cm.

What is the length of the corresponding side in the larger polygon?

The corresponding side is 20 cm

300

In triangle ABC, angle A = 40°, angle B = 60°, and side a = 10 cm. Find side b.


Answer:

b ≈ 13.47 cm


300

Find the surface area of a cube with side

=6x62

6 cm

=6x36

= 216 cm?

300

A square has a side length of 6 units. A circle of radius 3 units is drawn inside the square so that it touches all four sides (it’s inscribed).

What is the probability that a randomly chosen point inside the square also lies inside the circle



  • Area of square: 6 \times 6 = 36
  • Area of circle: \pi \times 3^2 = 9\pi
  • Probability:
    P = \frac{9\pi}{36} = \frac{\pi}{4}


400

Quadrilateral ABCD is congruent to quadrilateral WXYZ. If side AB = 7 cm, angle B = 90°, and side CD = 5 cm, what are the measures of side WX, angle X, and side YZ?


  • Side WX = Side AB = 7 cm
  • Angle X = Angle B = 90°
  • Side YZ = Side CD = 5 cm


400

The dimensions of Rectangle A are 4 cm by 6

CT.

The length of Rectangle B is 10 cm.

What is the width of Rectangle B?

The width of rectangle B is 6.67 cm

400

In triangle XYZ, side x = 7 cm, y = 9 cm, z = 10 cm. Find angle X.


Answer:

X ≈ 42.8°


400

Find the surface area of a rectangular prism with dimensions:

length = 8 cm, width = 5 cm, height = 3

cm

Calculation:

=2(8x5+8x3+5x3)

=2(40 + 24 + 15)

= 2(79)

= 158 cm2

400

A circle with radius 5 units is drawn. A square is inscribed in the circle (all four vertices touch the circle).

What is the probability that a randomly chosen point inside the circle also lies inside the square?



  • Radius of circle = 5
  • Area of circle = \pi \times 5^2 = 25\pi
  • Side length of inscribed square = 5\sqrt{2} \times 2 = 10\sqrt{2}, but that’s too long. Let’s fix it properly:


500

Two triangles, ΔABC and ΔDEF, are congruent. If angle A = 40°, angle B = 60°, and side AB = 5 cm, what are the measures of angles D and E, and the length of side DE?


  • Angle D = Angle A = 40°
  • Angle E = Angle B = 60°
  • Side DE = Side AB = 5 cm


500

The area of the smaller triangle is 27 cm?.

What is the area of the larger triangle?

(Hint: Areas scale by the square of the scale factor)

The area of the larger triangle is 75cm2

500

In a right triangle, angle A = 30°, hypotenuse = 10 cm. Find the length of the side opposite angle A.


Answer:

Opposite side = 5 cm


500

Find the volume of a cylinder with radius = 4

cm and height = 10 cm

(Use nt = 3.14)

Calculation:

=3.14 × 42 × 10

= 3.14 × 16 × 10

= 3.14 × 160

= 502.4 cmg

500

A point is chosen at random inside a rectangle that is 10 units long and 4 units wide. A circle with radius 2 units is drawn completely inside the rectangle.

What is the probability that the point lands inside the circle?



  • Area of rectangle = 10 \times 4 = 40
  • Area of circle = \pi \times 2^2 = 4\pi
  • Probability = \frac{4\pi}{40} = \frac{\pi}{10}


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