Section 1
Classifying Triangles
Classify each triangle by its angle measures.(IMAGE CAN'T COPY).In $\triangle J K L, J K, K L,$ and $J L$ are equal. How does this help you classify $\triangle J K L$ byits side lengths?
Apply the vocabulary from this lesson to answer each question.$\triangle X Y Z$ is an obtuse triangle. What can you say about the types of angles in $\triangle X Y Z?$
Classify each triangle by its angle measures.$\triangle D B C$
Classify each triangle by its angle measures.$\triangle A B D$
Classify each triangle by its angle measures.$\triangle A D C$
Classify each triangle by its side lengths.$\triangle E G H$
Classify each triangle by its side lengths.$\triangle E F H$
Classify each triangle by its side lengths.$\triangle H F G$
Find the side lengths of each triangle.
Find the side lengths of each triangle.(TRIANGLE NOT COPY)
A jeweler creates triangular earrings by bending pieces of silver wire. Each earring is an isosceles triangle with the dimensions shown. How many earrings can be made from a piece of wire that is 50 cm long?
Classify each triangle by its angle measures.$\triangle B E A$
Classify each triangle by its angle measures.(ANGLE NOT COPY)$\triangle A B C$
Classify each triangle by its side lengths.$\triangle P S T$
Classify each triangle by its side lengths.$\triangle R S P$
Classify each triangle by its side lengths.$\triangle R P T$
Draw a triangle large enough to measure. Label the vertices $X, Y,$ and $Z .$a. Name the three sides and three angles of the triangle.b. Use a ruler and protractor to classify the triangle by its side lengths and angle measures.
Use the following information for Exercises 21 and 22 A manufacturer makes trusses, or triangular supports, for the roofs of houses. Each truss is the shape of an isosceles triangle in which $\overline{P Q} \cong \overline{P R}$. The length of the base $\overline{Q R}$ is $\frac{4}{3}$ the length of each of the congruent sides.The perimeter of each truss is $60 \mathrm{ft}$. Find each side length.
Use the following information for Exercises 21 and 22 A manufacturer makes trusses, or triangular supports, for the roofs of houses. Each truss is the shape of an isosceles triangle in which $\overline{P Q} \cong \overline{P R}$. The length of the base $\overline{Q R}$ is $\frac{4}{3}$ the length of each of the congruent sides.How many trusses can the manufacturer make from 150 feet of lumber?
Draw an example of each type of triangle or explain why it is not possible.isosceles right
Draw an example of each type of triangle or explain why it is not possible.equiangular obtuse
Draw an example of each type of triangle or explain why it is not possible.scalene right
Draw an example of each type of triangle or explain why it is not possible.equilateral acute
Draw an example of each type of triangle or explain why it is not possible.scalene equiangular
Draw an example of each type of triangle or explain why it is not possible.isosceles acute
An equilateral triangle has a perimeter of 105 in. What is the length of each side of the triangle?
Classify each triangle by its angles and sides.$\triangle A B C$
Classify each triangle by its angles and sides.$\triangle A C D$
An isosceles triangle has a perimeter of $34 \mathrm{cm}$. The congruent sides measure $(4 x-1) \mathrm{cm} .$ The length of the third side is $x \mathrm{cm} .$ What is the value of $x ?$
The base of the Flatiron Building is a triangle bordered by three streets: Broadway, Fifth Avenue, and East Twenty-second Street. The Fifth Avenue side is 1 ft shorter than twice the East Twenty-second Street side. The East Twenty-second Street side is $8 \mathrm{ft}$ shorter than half the Broadway side. The Broadway side is $190 \mathrm{ft}$.a. Find the two unknown side lengths.b. Classify the triangle by its side lengths.
Thinking Is every isosceles triangle equilateral? Is every equilateral triangle isosceles? Explain.
Tell whether each statement is sometimes, always, or never true. Support your answer with a sketch.An acute triangle is a scalene triangle.
Tell whether each statement is sometimes, always, or never true. Support your answer with a sketch.A scalene triangle is an obtuse triangle.
Tell whether each statement is sometimes, always, or never true. Support your answer with a sketch.An equiangular triangle is an isosceles triangle.
Write a formula for the side length $s$ of an equilateral triangle, given the perimeter $P$. Explain how you derived the formula.
Use the method for constructing congruent segments to construct an equilateral triangle.
This problem will prepare you for the Concept Connection on page 238 . Marc folded a rectangular sheet of paper, $A B C D,$ in half along $\overline{E F}$. He folded the resulting square diagonally and then unfolded the paper to create the creases shown.a. Use the Pythagorean Theorem to find $D E$ and $C E$b. What is the $\mathrm{m} \angle D E C ?$c. Classify $\triangle D E C$ by its side lengths and by its angle measures.
What is the side length of an equilateral triangle with a perimeter of $36 \frac{2}{3}$ inches?A. $36 \frac{2}{3}$ inchesB. $18 \frac{1}{3}$ inchesC. $12 \frac{1}{3}$ inchesD. $12 \frac{2}{9}$ inches
The vertices of $\triangle R S T$ are $R(3,2), S(-2,3),$ and $T(-2,1) .$ Which of these best describes $\triangle R S T$F. IsoscelesG. ScaleneH. EquilateralJ. Right
Which of the following is NOT a correct classification of $\triangle L M N ?$A. AcuteB. EquiangularC. IsoscelesD. Right
$\triangle A B C$ is isosceles, and $\overline{A B} \cong \overline{A C} . A B=\left(\frac{1}{2} x+\frac{1}{4}\right),$ and $B C=\left(\frac{5}{2}-x\right) .$ What is the perimeter of $\triangle A B C ?$
A triangle has vertices with coordinates $(0,0),(a, 0),$ and $(0, a),$ where $a \neq 0$ Classify the triangle in two different ways. Explain your answer.
Write a two-column proof. Given: $\triangle A B C$ is equiangular. $E F \| A C$ Prove: $\triangle E F B$ is equiangular.
Two sides of an equilateral triangle measure $(y+10)$ units and $\left(y^{2}-2\right)$ units. If the perimeter of the triangle is 21 units, what is the value of $y ?$
The average length of the sides of $\triangle P Q R$ is $24 .$ How much longer then the average is the longest side?
Name the parent function of each function.$$y=5 x^{2}+4$$
Name the parent function of each function.$$2 y=3 x+4$$
Name the parent function of each function.$$y=2(x-8)^{2}+6$$
Determine if each biconditional is true. If false, give a counter example.Two lines are parallel if and only if they do not intersect.
Determine if each biconditional is true. If false, give a counter example.A triangle is equiangular if and only if it has three congruent angles.
Determine if each biconditional is true. If false, give a counter example.A number is a multiple of 20 if and only if the number ends in a $0 .$
Determine whether each line is parallel to, is perpendicular to, or coincides with $y=4 x$.$$y=4 x+2$$
Determine whether each line is parallel to, is perpendicular to, or coincides with $y=4 x$.$$4 y=-x+8$$
Determine whether each line is parallel to, is perpendicular to, or coincides with $y=4 x$.$$\frac{1}{2} y=2 x$$
Determine whether each line is parallel to, is perpendicular to, or coincides with $y=4 x$.$$-2 y=\frac{1}{2} x$$