Question

50 POINTS PLS HELP

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle ADC is congruent to triangle CBA given that ∠D and ∠B are right angles and DC is parallel to AB. Upload the entire proof below.

Given:

∠D and ∠B are right angles

DC || AB

Prove:

△ADC ≅ △CBA



STATEMENT REASON
1.∠D and ∠B are right angles 1. Given
2. 2. If lines are parallel, then alternate interior angles
are equal
3. 3.
4. 4. Hypotenuse Angle Theorem

Answer 1

To prove triangle ADC is congruent to triangle CBA, we establish that the pairs of corresponding angles are congruent due to the parallel lines, and the sides opposite the right angles are congruent, then apply the Hypotenuse-Angle Theorem.

Step-by-step explanation:

Two-Column Proof for Congruent Triangles

To prove that triangle ADC is congruent to triangle CBA, given that ∠D and ∠B are right angles and line DC is parallel to AB, we can use the following two-column proof:

1. ∠D and ∠B are right angles. - Given
2. DC || AB - Given
3. Angle D is congruent to ∠C (Alternate Interior Angles are congruent since DC || AB). - If lines are parallel, then alternate interior angles are equal.
4. DC is congruent to AB (Sides in a rectangle are congruent since ∠D and ∠B are right angles). - Definition of a rectangle.
5. Triangle ADC is congruent to triangle CBA (Hypotenuse-Angle Congruence). - The Hypotenuse Angle Theorem states that if a triangle has one right angle and an acute angle congruent to an acute angle in another right-angled triangle, then the triangles are congruent.

This proof demonstrates that triangle ADC is congruent to triangle CBA by the Hypotenuse-Angle Theorem, given the parallel lines and the right angles.

Answer 2

Step-by-step explanation:

type the prove that you took in school because some of them you may not have been taught in your school

STATEMENT REASON

∠D and ∠B are right angles 1. Given

∠D = ∠B 2. If lines are parallel, then alternate interior angles are equal

∠D + ∠C + ∠B = 180° 3. Sum of angles in a triangle is 180°

∠D + ∠C + ∠B = 180° 4. Hypotenuse Angle Theorem

∠C = ∠C 5. Reflexive Property

△ADC ≅ △CBA 6. SAS Congruence Theorem