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Step-4

Title: Proving Special Angle Pairs

Grade: 10-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	If two angles are complementary to the same angle, then they are congruent to each other. $4$
2	Step	Assume	Let us assume that \$\angle POQ\$ is complementary to \$\angle AOP\$ and \$\angle QOR\$.
3	Step	Definition of complementary angles	\$\angle POQ + \angle AOP = 90°\$ and \$\angle POQ + \angle QOR = 90°\$.
4	Step	From the above two equations, we can say that	\$\angle POQ + \angle AOP = \angle POQ + \angleQOR\$.
5	Step	Now subtract \$\angle POQ\$ from both sides	\$\angle AOP = \angle QOR\$
6		Answer	Hence, the theorem is proved

Step

Type

Explanation

Answer

Problem

If two angles are complementary to the same angle, then they are congruent to each other.
$4$

Step

Assume

Let us assume that \$\angle POQ\$ is complementary to \$\angle AOP\$ and \$\angle QOR\$.

Step

Definition of complementary angles

\$\angle POQ + \angle AOP = 90°\$ and \$\angle POQ + \angle QOR = 90°\$.

Step

From the above two equations, we can say that

\$\angle POQ + \angle AOP = \angle POQ + \angleQOR\$.

Step

Now subtract \$\angle POQ\$ from both sides

\$\angle AOP = \angle QOR\$

Answer

Hence, the theorem is proved