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Step-3

Title: Proving Special Angle Pairs

Grade: 10-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	Vertical angles theorem: vertical angles are congruent. $3$
2	Step	Given	Line k and m intersect
3	Step	Prove	\$\angle 1 \cong \angle 3\$ , and \$\angle 2 \cong \angle 4 \$
4	Step	Definition of linear pairs	\$\angle 1 and \angle 2\$ , \$\angle 2 and \angle 3\$ are linear pairs
5	Step	Linear pair postulate	\$\angle 1 and \angle 2\$ are supplementry and \$\angle 2 and \agle 3\$ are supplementry
6	Step	supplementry of the same angle theorem	\$\angle 1 \cong \angle 3\$

Step

Type

Explanation

Answer

Problem

Vertical angles theorem: vertical angles are congruent.
$3$

Step

Given

Line k and m intersect

Step

Prove

\$\angle 1 \cong \angle 3\$ , and \$\angle 2 \cong \angle 4 \$

Step

Definition of linear pairs

\$\angle 1 and \angle 2\$ , \$\angle 2 and \angle 3\$ are linear pairs

Step

Linear pair postulate

\$\angle 1 and \angle 2\$ are supplementry and \$\angle 2 and \agle 3\$ are supplementry

Step

supplementry of the same angle theorem

\$\angle 1 \cong \angle 3\$