Improve Your Geometry Skills with Practice Problems

If ${\displaystyle \sin x=e^y,0<x<\pi ,}$ what is dy/dx in terms of x?
(A) ${\displaystyle -\tan x}$
(B) ${\displaystyle -\cot x}$
(C) ${\displaystyle \cot x}$
(D) ${\displaystyle \tan x}$
(E) ${\displaystyle \csc x}$

A tributary joins a river at an angle. Find the value of x.

Simplify the expression ${\displaystyle \frac{\sec x}{\sin x}-\frac{\sin x}{\cos x}}$

To calculate:The ratio of line AB and BC.
Given information:
The following diagram is given

Solve the equation $\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}={\left(\frac{1-\tan A}{1-\cot A}\right)}^2={\tan }^{2}A$

Write a simplitiead expression for the length of QR.
13y+25
8y+5
QR= ​

Determine whether ${\displaystyle \mathrm{△}ABC\text{and}\mathrm{△}DEF}$ are similar for each set of measures. If so, identify the similarity criterion.
1.${\displaystyle m\mathrm{\angle }A=20,m\mathrm{\angle }C=20,m\mathrm{\angle }D=40,m\mathrm{\angle }F=40}$
2.${\displaystyle m\mathrm{\angle }A=20,m\mathrm{\angle }C=4u,m\mathrm{\angle }D=20,m\mathrm{\angle }F=40}$
3.${\displaystyle AB=20,BC=40,m\mathrm{\angle }B=53}$,
${\displaystyle DE=10,EF=20,m\mathrm{\angle }E=53}$

${\displaystyle \text{Let}over\to \left\{e_1\right\},over\to \left\{e_2\right\},over\to \left\{e_3\right\}\text{be standard unit vectors along the coordinate axes in}{R}^3.\text{Let S and T be the linear transformations defind in}{R}^3.\text{Show that if}}$
${\displaystyle S(over\to {\left\{e\right\}}_1)=T(over\to {\left\{e\right\}}_1),S(over\to {\left\{e\right\}}_2)=T(over\to {\left\{e\right\}}_2),S(over\to {\left\{e\right\}}_3)=T(over\to {\left\{e\right\}}_3)}$
then
${\displaystyle S(over\to \left\{x\right\})=T(over\to \left\{x\right\})}$
for any ${\displaystyle over\to \left\{x\right\}\in R^3}$

Prove: ${\displaystyle \mathrm{△}CBF\stackrel{\sim }{=}\mathrm{△}EDF}$ using isometric (rigid) transformations.
Outline the necessary transformations to prove ${\displaystyle \mathrm{△}CBF\stackrel{\sim }{=}\mathrm{△}EDF}$ using a paragraph proof. Be sure to name specific sides or angles used in transformation and any congruency statements.

Solve the equation $\frac{1-\sin x}{1+\sin x}=(\sec x-\tan x{)}^2$

Foci: (0,0), (0,8), major axis of length 16

Given tanx is ${\displaystyle \frac{3}{4}}$. you can use the double formula to find ${\displaystyle \tan 2x}$. the teacher wants us to find 3 other doubles like ${\displaystyle \sin 2x}$ or ${\displaystyle \cos 2x}$ without using the double angle formulas.

Using Similarity Express x in terms of a, b, and c.
Given:
The given pair of triangles is similar.
The given pair of triangle is,

An inverted cone (base above the vertex) is 2 m high and has a base radius of ${\displaystyle \frac{1}{2}}$ m. If the tank is full, how much work is required to pump the water to a level 1 m above the top of the tank?

Describe one similarity and one difference between the definitions of ${\displaystyle \sin 0,\text{and}\cos 0}$, where 0 is an acute angle of a right triangle.

Solve the following systems of congruences.
$x\equiv 2(mod5)$

Check whether the given dilationis a similarity transformation or not.
Given:
The given dilation is

Are pairs of triangles similar?
Given information:

Given ${\displaystyle \mathrm{△}DEF\text{and}\mathrm{△}EGF}$ in the diagram below, determine if the triangles are similar. If so, write a similarity statement, and state the criterion used to support your claim.

In this problem, allow $T1:RR2\to RR2\text{ and }T2:RR2\to R2$ be linear transformations. Find $Ker(T_1),Ker(T_2),Ker(T_3)$ of the respective matrices
$A=[(1,-1),(-2,0)],B=[(1,5),(-2,0)]$