Improve Your Geometry Skills with Practice Problems

In quadrant I, drawn a right triangle with one leg on the x-axis and its hypotenuse on the terminal side of drawn in standard position. If $\sin =\frac{7}{25}$, then what is the value of $\theta$?

Solve the congruence equation:
2x=3 mod 5

Solve the equation $\sec x-\sec xsi{n}^{2}x=\cos x$

For each of the following congruences, find all integers N, with N>1, that make the congruence true.
$23\equiv 22(modN)$.

Write a conic section with polar equation the focus at the origin and the given data hyperbola, eccentricity 2.5, directrix y = 2

What does the combined length of any two sides of a triangle exceed?

In ${\displaystyle △PQR,m\angle P=46x}$ and ${\displaystyle m\angle R=7x}$,
a. Write and solve an equation to find the measure of each angle.
b. Classify the triangle based on its angles.

‘Rewrite the Jofinition “An equilateral triangle has three sides vrite the definihon fv, biconditional.

Show the similarity ${\displaystyle \int \frac{x}{{(x^2+a^2)}^m}dx=\frac{1}{2(-m+1){(x^2+a^2)}^{m-1}}+C}$ using the substitution ${\displaystyle u=x^2+a^2}$. Also check that the integration is correct by deriving the answer.

Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not. write no congruence can be deduced.

In the roof truss shown, AB = 8 and ${\displaystyle m\mathrm{\angle }HAF={37}^{\circ }}$. Find: ${\displaystyle m\mathrm{\angle }ADB}$.
(HINT: The design of the roof truss displays line symmetry.)

Solve ${\displaystyle \sin 3x+\frac{\sin x}{\cos x}+\cos 3x=\tan 2x}$

How are the inverse trigonometric functions defined?

Triangle MPT with ${\displaystyle \overline{NR}\mid \mid \overline{MT}}$ is shown below. The dimensions are in centimeters.

Which measurement is closest to the length of ${\displaystyle \overline{RT}}$ in centimeters?
1)1.4
2)1.8
3)3.4
4)4.3

A packing box is 3.5 feet by 1.4 feet by 1.8 feet. A box that is 3.1 feet by 1.1 feet by 1.4 feet is placed inside the first box. The rest of the box is filled with packing foam. How many cubic feet does the packing foam take up?

Given:
${\displaystyle \theta ={240}^{\circ }}$
Find the value of ${\displaystyle \theta }$ in radians (in terms of ${\displaystyle \pi }$)

How many lines of symmetry does the figure shown at the right have?
A) 0
B) 1
C) 5
D) 10

The perimeter of a rectangle is 56 in. The ratio of the length to the width is 6:1. Find the length and the width.

Proving Similarity In the figure CDEF is a rectangle. Prove that ${\displaystyle \mathrm{△}ABC\sim \mathrm{△}EBF}$.
Given:
The given figure is,

Identify the graph of the nondegenerate conic sections: $4x^2-25y^2-24x+250y-489=0$.