Download Name: Date:______ Period:______ Triangle Theorems: Notes

Name:_______________________________
Triangle Theorems: Notes Packet
Date:________ Period:_______
Ms. Anderle
Triangle Theorems: Notes Packet
Exterior Angles of a Triangle:
Theorem: A measure of an _______________ angle of a triangle is equal to the _________ of the two
________________________________________.
Recall: An exterior angle is formed by one _____________ of a triangle and the ________________ of
an adjacent _______________ of the triangle.
Example:
Examples:
1) In ∆PQR, m<Q=45⁰, and m<R=72⁰. Find the measure of and exterior angle at P.
2) In ∆DEF, an exterior angle at F is represented by 8x + 15. If the two non-adjacent interior angles
are represented by 4x + 5, and 3x + 20, find the value of x.
3) Find the measure of an exterior angle at the base of an isosceles triangle whose vertex angle
measures 40⁰.
Triangle Inequality Theorem:
The triangle _________________ theorem states that the sum of the two ____________ sides of a
triangle is always _________________ than the largest side.
Example:
Examples:
1) The lengths of two sides of a triangle are 12 and 8, the length of the third side could be:
(1) 20
(2) 4
(3) 21
(4) 5
2) Which of the following sets of numbers could represent the sides of a triangle?
(1) {3,4,7}
(2) {8,10,19}
(3) {2,3,4}
(4) {1,1,3}
3) A box contains one 3-cm rod, one 7-cm rod, one 10-cm rod, and one 12-cm rod. What is the
maximum number of triangles that can be formed using the full length of the rods as sides?
4) In ΔABC, AB = BC. Which statement will always be true?
(1) m<B = m<A
(2) m<A > m<B
(3) m<A = m<C
(4) m<C < m<B
Sides & Angles of a Triangle:
In a triangle the shortest side is opposite the _____________ angle. The reverse is also true, the
_______________ side is opposite the largest angle.
Example:
Examples:
For the examples below, state the largest and smallest angles of the triangle. Diagrams are not
drawn to scale.
For the examples below, state the longest and shortest sides of the triangle. Diagrams are not
drawn to scale.
6) In ΔWXY <W=98 and <Y=49, what is the largest side of this triangle?
7) In ΔPQR, PQ=8, QR=12, and RP=13. Which statement about the angles of ΔPQR must be true?
(1) m<Q > m<P > m<R
(3) m<R > m<P > m<Q
(2) m<Q > m<R > m<P
(4) m<P > m<R > m<Q
8) In ΔQRS m<Q = 6x - 5, m<R = 3x + 7, x + 8. Which side is the largest side of the triangle? Which side
the smallest side of the triangle?
9) In ΔSTU, ST = 12, TU = 13, and US = 20. Which angle is the largest angle of the triangle? Explain.