The triangle ABC is an isosceles triangle. What are each

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

What do all these triangles have in common?
a)
b)
c)

Given a right triangle. anglea is ${\displaystyle {51}^{\circ }}$. A line is drawn from anglec ${\displaystyle \left({90}^{\circ }\right)}$ to the hypotenuse, creating a ${\displaystyle 7^{\circ }}$ angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

State the form of the law of cosines used to solve a triangle for which all three sides are given (SSS).

Solve each of the following triangles. If there are two triangles, solve both. Round angle measurements to one decimal place and side lengths to two decimal places. ${\displaystyle a=9,b=4,B={23}^{\circ }}$
a=
y=
c=

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.

The diagonals of a trapezoid divide each other proportionally.

Given: Trapezoid ABCD with diagonal AC, BD intersecting at O
Prove: ${\displaystyle \frac{AO}{CO}=\frac{BO}{DO}}$
$$\begin{array}{|cc|}\hline \text{Statements}& \text{Reasons}\\ 1.(seeabove)& \text{1. Given}\\ 2.& 2.\\ 3.\text{(Give 2 pairs of equal angles)}& \text{3. If two parallel lines are cut by a transveral,}\\ & \text{then the alternate interior angles are=.}\\ 4.\mathrm{△}AOB\sim \mathrm{△}COD& 4.\\ 5.\frac{AO}{CO}=\frac{BO}{DO}& 5.\\ \hline\end{array}$$