TWO COLUMN TRIANGLE PROOF
Given: line AB is parallel to line DE, and line AD bisects line BE
Prove: triangle ABC is congruent to triangle DEC by using the ASA (angle-side-angle) postulate
You have opposite angles are equal, and alternate interior angles equal, and the line is bisectd so sides are equal. That is ASA. YOu can put this into proof format.
To prove that triangle ABC is congruent to triangle DEC using the ASA postulate, you need to show that they have two corresponding pairs of congruent angles and a pair of congruent sides.
Here's a step-by-step explanation of how to approach the proof:
Step 1: Given Statement
Write down the given statement: line AB is parallel to line DE, and line AD bisects line BE.
Step 2: Identify Congruent Angles
Since AD bisects line BE, angle BAD is congruent to angle ADE. This is because the bisector of a line segment divides the angles into two congruent angles.
Step 3: Identify Corresponding Sides
Since AB is parallel to DE, line segment AB is parallel to line segment DE. Therefore, line segment AB is congruent to line segment DE.
Step 4: Identify Congruent Angles
One of the angles of triangle ABC is angle ABC. The other corresponding angle in triangle DEC is angle DEC.
Step 5: Write the Proof Statement
Write the proof statement using the congruent angles and side identified above:
Angle BAD is congruent to angle ADE (from step 2),
AB is congruent to DE (from step 3),
Angle ABC is congruent to angle DEC (from step 4).
Step 6: State the Congruence Criterion
Finally, state the congruence criterion used in the proof. In this case, it is the ASA (angle-side-angle) postulate.
Therefore, by the ASA postulate, triangle ABC is congruent to triangle DEC.