Geometry - SIMILAR POLYGONS
Find the diagonal of a cube if its side equals 5. When applicable, simplify radicals and show all of your work.
In order to find the diagonal of the cube, first solve for the diagonal of the base: 5^2 + 5^2 = c^2 c = 5√2 Now solve for the diagonal of the cube: 5^2 + (5√2)^2 = x^2 25 + 50 = x^2 x^2 = 75 x = 5√3
Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your work.
Leg = x Hypotenuse = 8 (√2)leg = hypotenuse (√2)x = 8 x = 8/√2 (√2/√2) = 8√2/2 = 4√2
If x/8 = 5/4, then x = 10.
True
Given: ΔABC is a right triangle. Line BC = 5, line AC = 20 Determine the length of the missing side of ΔABC. When applicable, simplify radicals and show all of your work.
Use Pythagorean theorem to find the missing side of the right triangle: AB^2 + BC^2 = AC^2 AB^2 + 5^2 = 20^2 AB^2 + 25 = 400 AB^2 = 375 AB = 5√15
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation. (xᵒ, 13)
Use cosine to solve for the measure of the missing angle, x, since the two given sides are adjacent (12) and hypotenuse (13). cos xᵒ = 12/13
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation. (80ᵒ, 9)
Use sine to solve for x since the given side is the opposite side (9) and the missing side is the hypotenuse (9): sin 80ᵒ = 9/x
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation. (70ᵒ, 8)
Use sine to solve for x since the missing side is the opposite side (x) and the given side is the hypotenuse (8): sin 70ᵒ = x/8
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation. (xᵒ, 24)
Use tangent to solve for the measure of the missing angle, x, since the two given sides are opposite (7) and adjacent (24). tan xᵒ = 7/24
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation. (35ᵒ, 9)
Use tangent to solve for x since the given side is the opposite side (9) and the missing side is the adjacent side (x): tan 35ᵒ = 9/x
Enter the trigonometric equation you would use to solve for x. Do not solve the equation.
When solving for a missing length of a right triangle, use trigonometric ratios: sine = opposite/hypotenuse cosine = adjacent/hypotenuse tangent = opposite/adjacent Use tangent to solve for x since the missing side is the opposite side (x) and the given side is the adjacent side (12): tan 20ᵒ = x/12
Complete this proof. Given: a | | b Prove: ΔMOP ~ ΔRON
a | | b - Given ∠1 = ∠2, ∠3 = ∠4 - Alt. interior ∠s are = ΔMOP ~ ΔRON - AA
Complete this proof. Given: line EC is perpendicular to line AC, line DB is perpendicular to line AC, ∠A = ∠F Prove: ΔMDF ∼ ΔNCA
line EC is perpendicular to line AC, line DB is perpendicular to line AC - Given line EC | | line DB - Two lines perpendicular to same line are | | ∠1 = ∠2 - Alt. interior ∠s are = ∠A = ∠F - Given ΔMDF ∼ ΔNCA - AA
Solve x/3 = x+2/2 x =
-6
Match the following. 1. Cosine ratio 2. Projection of a segment on a line 3. Geometric mean 4. Projection of a point on a line 5. Ratio 6. Proportion 7. Similar polygons 8. Tangent ratio 9. Sine ratio
1. In a right triangle, the side adjacent to an acute angle over the hypotenuse. 2. The portion of a line with endpoints that are the projections of the endpoints of the segment. 3. For any positive real numbers a, b, and x if then x is called the geometric mean between a and b. 4. The point where a perpendicular through the point to the line intersects the line. 5. The comparison of two numbers by division. The quotient is the ratio of the two numbers. 6. An equation that states that two ratios are equal. 7. Polygons whose vertices can be matched in a one-to-one correspondence so that corresponding angles are equal and corresponding sides are in proportion. 8. In a right triangle, the side opposite an acute angle over the side adjacent to the acute angle. 9. In a right triangle, the side opposite an acute angle over the hypotenuse.
Find the missing measures. Given: ABC is a right triangle. AB = 6, BC = 8 , AC =
10
Solve the proportion for x . When applicable, simplify all radicals and show all of your work. 3/x = x/4
3/x = x/4 x^2 = 12 x = √12 = 2√3
