4.1 Triangles Notes Follow Up
Honors Geometry
Name: ________________________________
The Triangle Sum Theorem states the following: The sum of the measures of the interior angles of a triangle is
180°. Complete the following proof of the Triangle Sum Theorem below. Begin the proof by sketching a line
passing through D and parallel to AC . (p.219)
Given: # ABC
Prove: m1  m2  m3  180
PLAN FOR PROOF:
a. Draw an auxillary line through B and parallel to ̅̅̅̅
𝑨𝑪
b. Show that m∠𝟒 + m∠𝟐 + m∠𝟓 = 180°, ∠𝟏 ≅ ∠𝟒, and ∠𝟑 ≅ ∠𝟓
c. By substitution, 𝐦∠𝟏 + 𝐦∠𝟐 + 𝐦∠𝟓𝟑 = 𝟏𝟖𝟎
STATEMENTS
REASONS
1. What is a Polygon? What is a triangle?
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2. What is an auxiliary line and how was it used in the first proof?
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The Exterior Angle Theorem states the following: The measure of an exterior angle of a triangle is equal to the
sum of the measures of the two nonadjacent interior angles. Complete the following proof of the Exterior Angle
Theorem below. In the figure, 4 is the exterior angles and 1 & 2 are the nonadjacent interior angles.
Given: # ABC
Prove: m1  m2  m4
STATEMENTS
REASONS
1. ∆ABC
1. Given
2.
2. Triangle Sum Theorem
3. ∠3 and∠4 are supp
3.
4. m∠3 + m∠4 = 180°
4.
5.
5. Substitution
6. m∠1 + m∠2 = m∠4
6. Subtraction
3. How many different exterior angles does every triangle have?
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4. What is a corollary to a theorem?
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Corollary to the Triangle Sum Theorem states
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Prove the Corollary to the Triangle Sum Theorem below.
Given: # ABC
Prove: mB  mC  90
STATEMENTS
REASONS
1. ∆ABC
1. Given
BASIC TRIANGLE REVIEW
5. Triangles can be classified by side and by angle. Describe the different classifications by side. Include a
sketch of each classification.
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6. Describe the different classifications by angle. Include a sketch of each classification.
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7. Explain why an obtuse triangle cannot have two obtuse angles.
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8. An isosceles triangle is defined as a triangle with at least two congruent sides. What does this imply about an
equilateral triangle?
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