Download Sum of Angle Measure in a Triangle

Aim: What is the sum of angle measures in a triangle?
Do Now:
Given: DBE || AC
Prove: mA  my mC  180
Statements
1) DBE || AC
2) mDBE  180
B
x y z
D
A
E
C
Reasons
1) Given
2) Def. straight angle
3) mDBE  mx  my  mz 3) Partition Postulate
4) mx  my  mz  180
5) mx  mA, mz  mC
4) Substitution Post.
5) If || lines are cut by a
6) mA  my  mC  180
transv., alt. int. 's are  .
6) Substitution Post.
1
Theorem #19:
The sum of the measure of the angles of a triangle is 180°.
Corollary #19-1:
If two angles of one triangle are congruent to two angles of
another triangle, then the third angles are congruent.
B
F
C
A
G
E
If A  E, and C  G, then ...B  F .
Corollary #19-2:
The acute angles of a right triangle are complementary.
B
If ABC is a right triangle and
C
mC  90, then mA  mB  ...90.
A
Geometry Lesson: Sum of Angles in
a Triangle
2
Corollary #19-3:
Each acute angle of an isosceles right triangle measures 45°.
B
C
A
If ABC is an isosceles right triangle,
then mA  mB  ...
45
Corollary #19-4:
Each acute angle of an equilateral triangle measures 60°.
C
If ABC is an equilateral trianlge,
then mA  mB  mC  ...60.
A
B
Geometry Lesson: Sum of Angles in
a Triangle
3
Corollary #19-5:
The sum of the measures of the angles of a quadrilateral is 360°.
C
Given quadrilateral ABCD,
mA  mB  mC  mD  ...
360
D
A
B
Geometry Lesson: Sum of Angles in
a Triangle
4
Ex: Sum of Angle Measures in Triangles
1) In each case, state whether the 3 numbers can represent
the angle measures of a triangle.
a) 10, 120, 50 b) 65, 55, 65 c) 82, 14, 78
2) In EFG, EF  FG. If mE  48, determine the measures
of F and G.
3) Find the measure of the largest angle of a triangle if it’s
angle measures are in the ratio 1 : 3 : 5
4) The measure of the vertex angle of an isosceles triangle is
20 less than twice the measure of a base angle. Find the
measures of all angles in the triangle.
5) The degree measures of a triangle are represented
by 4 x  10, 2 x  5, and 3x  5. Show that the triangle
5
is a right triangle.