Question

PLEASE HELP ME!!!!!!!

Proof
Given: C
is the midpoint of DT¯¯¯¯¯¯¯¯
and DH¯¯¯¯¯¯¯¯¯∥UT¯¯¯¯¯¯¯

Prove: overlineCH≅CU¯¯¯¯¯¯¯¯

Answer 1

Answers:

1. Given
2. Definition of Midpoint
3. Alternate Interior Angles Theorem
4. Vertical Angles are Congruent
5. AAS
6. CPCTC

Step-by-step explanation

1. Always start with the given. Yes it seems silly to repeat exactly what your teacher wrote, but it's just how geometry proofs work. It helps to break up each given statement on its own separate line.
2. The midpoint splits the segment into two smaller equal halves. For example, if DT was 20 units long, then pieces DC and TC would be 10 units each.
3. Segments DH and UT are parallel. By the alternate interior angles theorem, we know that angles TUC and DHC are congruent. These angles are inside the parallel lines and alternate on either side of the transversal.
4. Vertical angles form after intersecting two lines. They are opposite one another and always congruent. The angles do not have to align vertically.
5. AAS stands for "angle angle side". It's very similar to ASA, but notice the congruent sides (DC and TC) are not between the congruent angles. This is why we go for AAS. Teachers will often try to trick students when offering AAS and ASA.
6. After we prove the triangles are congruent, we can conclude the corresponding pieces are congruent using the rule CPCTC which stands for "Corresponding Parts of Congruent Triangles are Congruent". It would be like saying two houses are identical, so the front doors must be identical. House = triangle, front door = part of the triangle.

Extra notes:

• We cannot use HL (hypotenuse leg) because we don't know if these are right triangles or not.
• SAS and SSS can't be used since we only know information about one pair of congruent sides.