Classifying Triangles
Problems Following Power Point
Name:
[1] Classify the triangle by angle and side names both.
[2] A triangle is equilateral. Its sides have lengths 4n, 2n+10, and 7n-15. Draw a triangle and label with the
expressions. Find the value of n and the length of each side.
[3] Draw a triangle with a straightedge that satisfies the conditions stated. If no triangle can satisfy the conditions,
write not possible.
a. An acute isosceles triangle
b. A right isosceles triangle
c. A right scalene triangle
d. An acute scalene triangle
[4] Complete with always, sometimes, or never.
a)
b)
c)
d)
e)
f)
If a triangle is acute then it is ___________________ isosceles
If a triangle is right then it is ___________________ isosceles
If a triangle is scalene then it is ___________________ isosceles
If a triangle is obtuse, then it is ___________________ isosceles.
If a triangle is isosceles, then it is ___________________ equilateral
If a triangle is equilateral, then it is ___________________ isosceles.
[5] The lengths of the sides of a triangle are 3t, 5t-12, and t+20. Draw a triangle and label with the expressions. Find
three different values for n that will make the triangle isosceles and find the length of each side for each case.
[6] A triangle may be classified by its largest angle. A triangle that contains an obtuse angle is called an obtuse
triangle; if it contains a right angle it is called a right triangle; an acute triangle is a triangle in which each angle is an
acute angle. Equiangular – all angles have equal measures. In any triangle the sum of the three angles is 𝟏𝟖𝟎°.
For each of the following, the measures of the angles of ∆𝐴𝐵𝐶 are represented in terms of x. Find the value of x, the
measures of all three angles, and classify the triangle as acute, right, obtuse. Show equation and work. Extra Credit:
Use a protractor and draw
(a) m<A = 3x+8
m<B = x+10
m<C = 5x
(b) m<A = x+24
m<B = 4x+17
m<C = 2x-17
(c) m<A=3x-5
m<B=x+14
m<C=2x-9
[7] ∆𝐴𝐵𝐶 is equiangular. Find x and y using an algebraic approach -set up a system of equations and solve.
m<A = 3x+7y-16.1
m<B = 4(10y – x + 0.9)