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Geometry- Triangle Angle Theorems Assignment

Mathematics9 CardsCreated 4 months ago

This deck covers key concepts related to triangle angle theorems, including angle measures, exterior angles, and properties of parallel lines.

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What is the value of x?

98
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Key Terms

Term
Definition
What is the value of x?
98
What is the value of k?
10

What is the measure of ∠EGF?

What is the measure of ∠CGF?

65

115

What is the measure of ∠ABD?

c. 114

Which represents an exterior angle of triangle XYZ?

c. JXZ

Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°

Which statement justifies that angle XAB is congruent to angle ABC?

d. Alternate interior angles of parallel lines cut by a transversal are congruent.

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Geometry- Triangle Angle Theorems Assignment
TermDefinition
What is the value of x?
98
What is the value of k?
10

What is the measure of ∠EGF?

What is the measure of ∠CGF?

65

115

What is the measure of ∠ABD?

c. 114

Which represents an exterior angle of triangle XYZ?

c. JXZ

Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°

Which statement justifies that angle XAB is congruent to angle ABC?

d. Alternate interior angles of parallel lines cut by a transversal are congruent.

Which statements are always true regarding the diagram? Check all that apply.

-m∠3 + m∠4 = 180°
-m∠2 + m∠4 + m∠6 = 180°
-m∠2 + m∠4 = m∠5

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of angle ABC is _____.
The measure of angle BAC is _____.
The measure of angle ACB is _____.

60
50
70

Given: ΔABC
Prove: m∠ZAB = m∠ACB + m∠CBA
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.

We know that m∠ZAB + m∠CAB = 180° by the ______.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because ______ .
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the _____.

angle addition postulate
of the triangle angle sum theorem
subtraction property