Question

unit 2 lesson 7 cumulatives practice problems

1. tell whether the asa postulate or the aas theorem can be applied directly to prove the triangles are congruent. if the triangles cannot be proved congruent, write not possible.
2. what triangle congruence theorem could you use to prove triangle ade is congruent to triangle cbe?
3. han wrote a proof that triangle bcd is congruent to triangle dab. hans proof is incomplete. fill in the blanks to make the proof work.

dc || ab

• line ab is parallel to line dc and cut by transversal db. so angles cdb and abd are __________________________ and must be congruent.
• side db is congruent to side bd because theyre the __________________________
• angle a is congruent to angle c because theyre both right angles.
• by the __________________________ triangle congruence theorem, triangle bcd is congruent to triangle dab.

Explanation:

Step1: Alternate Interior Angles

When two parallel lines \(AB\parallel DC\) are cut by a transversal \(DB\), the alternate interior angles \(\angle CDB\) and \(\angle ABD\) are congruent.

Step2: Reflexive Property

Side \(DB\) is congruent to side \(BD\) because of the reflexive property (a segment is congruent to itself).

Step3: AAS Theorem

We have two angles (\(\angle CDB\cong\angle ABD\), \(\angle A\cong\angle C\)) and a non - included side (\(DB = BD\)). By the Angle - Angle - Side (AAS) triangle congruence theorem, \(\triangle BCD\cong\triangle DAB\).

Answer:

• Alternate interior angles
• Reflexive property
• AAS