Download Angles of a triangle - Villa Walsh Academy

ANGLES OF A TRIANGLE
3.4
A TRIANGLE IS THE FIGURE FORMED BY THREE
SEGMENTS JOINING THREE NONCOLLINEAR
POINTS
LET’S CLASSIFY THEM!
(PUT THEM INTO “CLIQUES”)
To classify them by their number of congruent sides, we have three
options:
•Scalene
•Isosceles
•Equilateral
LET’S CLASSIFY THEM!
(PUT THEM INTO “CLIQUES”)
To classify them by their number of congruent angles, we have four
options:
Acute
Obtuse
Right
Equiangular
AUXILIARY LINES: P.S. THEY EXIST.
Auxiliary lines are lines that can be added to a diagram to help in a proof…we’ll
need them for our next proof.
Theorem: The sum of the measures of the angles of a triangle is 180.
THE SUM OF THE MEASURES OF THE ANGLES OF A
TRIANGLE IS 180.
Given:
ABC
Prove: 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180
1. Through B, draw 𝐵𝐷 parallel to 𝐴𝐶
2. 𝑚∠𝐷𝐵𝐶 + 𝑚∠5 = 180;
𝑚∠𝐷𝐵𝐶 = 𝑚∠2 + 𝑚∠4
1. Through a point outside a line, there is exactly
one line II to the given line.
2. Angle Addition Postulate
COROLLARY: A STATEMENT THAT CAN BE PROVED EASILY BY
APPLYING A THEOREM
Corollary: If two angles of one triangle are congruent to two angles of another
triangle, then the third angles are congruent. (WHY?)
Corollary: Each angle of an equiangular triangle has measure 60. (WHY?)
Corollary: In a triangle, there can be at most one right angle or obtuse angle.
(WHY?)
Corollary: The acute angles of a right triangle are complementary. (WHY?)
NEW THEOREM! BUT FIRST, VOCABULARY
PREDICT THE THEOREM….THINK THINK THINK

THEOREM:
THE MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE
EQUALS THE SUM OF THE MEASURES OF THE TWO REMOTE
INTERIOR ANGLES