Question

Given: <1 and <2 are complementary. <1 and <3 are complementary

Prove: 22 = 23
Complete the proof.

Answer 1

Answers:

1st box:
`\boldsymbol{90}`

2nd box:
`\boldsymbol{90}`

3rd box:
`\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}`

===============================================

Step-by-step explanation:

Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.

By "corner", I refer to a 90 degree angle.

Since
`\angle 1\text{ and } \angle 2` are complementary, we know that
`\text{m}\angle 1+\text{m}\angle 2 = 90` simply by the definition of what it means to be complementary.

---------------

Through similar logic,
`\angle 1\text{ and } \angle 3` are complementary which means
`\text{m}\angle 1+\text{m}\angle3 = 90`

We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.

That's how we end up with
`\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3`

After this point, subtract
`\text{m}\angle1` from both sides to cancel them out. We'll be left with
`\text{m}\angle 2 = \text{m}\angle 3`, which concludes with
`\angle 2 \cong \angle 3` to show the two angles are congruent.