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Step-5

Title: Proving Special Angle Pairs

Grade: 10-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	The ray of CD and opposite rays EF and EG. $5$
2	Step	Assume that PQ and RS are the two parallel lines cut by a transversal LM. W, X, Y, Z are the angles created by a transversal At the intersection point on the straight lines PQ and LM
3	Step	PQ is the straight line equation-1	\$\angle W + \angle Z = 180°\$
4	Step	LM is the straight line equation-2	\$\angle X + \angleZ = 180°\$
5	Step	So, from (1) and (2), we get	\$\angle W = \angle x\$
6	Step	Again, at the intersection point on the straight lines RS and LM
7	Step	RS is the straight line equation-3	stemL[\angle W + \angle Z = 180°]
8	Step	LM is the straight line equation-4	\$\angle W + \angle Y = 180°\$
9	Step	So, from (3) and (4), we get	\$\angle Z = \angle Y\$
10	Step	Therefore, it is concluded that the alternate interior angles are congruent.
11		Answer	Hence, the theorem is proved

Step

Type

Explanation

Answer

Problem

The ray of CD and opposite rays EF and EG.
$5$

Step

Assume that PQ and RS are the two parallel lines cut by a transversal LM. W, X, Y, Z are the angles created by a transversal

At the intersection point on the straight lines PQ and LM

Step

PQ is the straight line equation-1

\$\angle W + \angle Z = 180°\$

Step

LM is the straight line equation-2

\$\angle X + \angleZ = 180°\$

Step

So, from (1) and (2), we get

\$\angle W = \angle x\$

Step

Again, at the intersection point on the straight lines RS and LM

Step

RS is the straight line equation-3

stemL[\angle W + \angle Z = 180°]

Step

LM is the straight line equation-4

\$\angle W + \angle Y = 180°\$

Step

So, from (3) and (4), we get

\$\angle Z = \angle Y\$

Step

Therefore, it is concluded that the alternate interior angles are congruent.

Answer

Hence, the theorem is proved