Question

Write a two column proof: given ab is perpendicular to cm, ab is perpendicular to db, db is congruent to cm, m is the midpoint of ab. Prove triangle amc is congruent to triangle mbd?

Answer 1

To prove that triangle AMC is congruent to triangle MBD, we can use the congruent triangles postulate. By showing that AM is congruent to MB, CM is congruent to DB, and CM is perpendicular to DB, we can conclude that triangle AMC is congruent to triangle MBD.

Step-by-step explanation:

To prove that triangle AMC is congruent to triangle MBD, we can use the congruent triangles postulate. Here is a step-by-step proof:

1. Given: AB is perpendicular to CM, AB is perpendicular to DB, DB is congruent to CM, M is the midpoint of AB.
2. Since M is the midpoint of AB, AM is congruent to MB.
3. By the transitive property, CM is congruent to DB.
4. Since AB is perpendicular to CM and AB is perpendicular to DB, we can conclude that CM is perpendicular to DB.
5. By the SAS congruence postulate, triangle AMC is congruent to triangle MBD.