Question 1173654
Absolutely! Let's provide a two-column proof for this geometry problem.

Given:

MA ⊥ AI
RS ⊥ AI
K is the midpoint of MT
Prove:

ΔMAK ≅ ΔTIK
Two-Column Proof:

Statement	Reason
1. MA ⊥ AI	Given
2. ∠MAI = 90°	Definition of perpendicular lines
3. RS ⊥ AI	Given
4. ∠RIS = 90°	Definition of perpendicular lines
5. ∠MAI = ∠RIS	Both are 90° angles
6. ∠TIK = ∠MAK	Vertical angles are congruent
7. K is the midpoint of MT	Given
8. MK = TK	Definition of midpoint
9. ∠TIK = ∠MAK	Vertical angles are congruent
10. ΔMAK ≅ ΔTIK	Angle-Side-Angle (ASA) Congruence Theorem (∠MAK, MK, ∠MKA and ∠TIK, TK, ∠TKI)

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Paragraph Proof:

We are given that MA is perpendicular to AI and RS is perpendicular to AI. This means that angles MAI and RIS are both 90 degrees, making them congruent. We are also given that K is the midpoint of MT, which means that line segments MK and TK are congruent. Since vertical angles are congruent, angle TIK is congruent to angle MAK. With angle MAK congruent to angle TIK, MK congruent to TK and angle MKA congruent to angle TKI, we can apply the Angle-Side-Angle (ASA) congruence theorem. Therefore, triangles MAK and TIK are congruent.