Given: △ABE has vertices at A(2,7), B(4,3), and E(1,4). Prove: △ABE is a right triangle.
Triangle A B E with vertices as described in the text.
Match each numbered statement with the correct reason

STATEMENTS
△ABE has vertices at A(2,7), B(4,3), and E(1,4).
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If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given
2. The slope of AB¯¯¯¯¯¯¯¯=3−74−2=−2.

The slope of BE¯¯¯¯¯¯¯¯=4−31−4=−13.

The slope of AE¯¯¯¯¯¯¯¯=4−71−2=3.
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If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given
3. (slope of AE¯¯¯¯¯¯¯¯)⋅(slope of BE¯¯¯¯¯¯¯¯)=−1
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If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given
4. AE¯¯¯¯¯¯¯¯⊥BE¯¯¯¯¯¯¯¯
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If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given
5. ∠E is a right angle.

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Select an option
If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given
6. △ABE is a right triangle.

REASONS
If the product of the slopes of two nonvertical lines is −1, the lines are perpendicular.
Multiply.
Definition of a right triangle
Slope formula
Perpendicular lines intersect to form right angles.
Given