Question

What is the missing reason in the proof? statement reason 1. ?egf ? ?hgk 1. vert. ?s are ? 2. kh ? ef 2. given 3. ?f ? ?k 3. alt. int. ?s are ? 4. g is the midpoint of kf 4. given 5. fg ? kg 5. def. of midpt. 6. ?feg ? ?khg 6. ? 7. hg ? eg 7. cpctc sas asa aas hl

Answer 1

The missing reason in the proof is CPCTC (Corresponding Parts of Congruent Triangles are Congruent). CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.

Step-by-step explanation:

The missing reason in the proof is CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.

In this proof, the missing reason can be used to conclude that triangles ∼FEG and ∼KHG are congruent, which justifies the statement HG ≅ EG.

Answer 2

Since G is the midpoint of KF and KH is parallel to EF, the missing reason in the proof is: C. ASA.

In Mathematics and Euclidean Geometry, ASA is an abbreviation for Angle-Side-Angle and it states that when two (2) angles and their included side in two triangles are congruent, then the triangles are said to be congruent.

Based on the angle, side, angle (ASA) congruence theorem, triangle FEG is congruent with triangle KHG based on the following statement and reasons in this two-column proof;

Statement Reason

1. ∠ EGF≌ ∠ HGK 1. Vertical angles are congruent

2. KH║EF 2. Given

3. ∠F ≌ ∠K 3. Alternate interior ∠s are ≅

4. G is the midpoint of KF 4. Given

5. FG ≌ KG 5. Definition of midpoint

6. △FEG ≌ △KHG 6. ASA

Complete Question:

The proof that HG ≅ EG is shown. Given: G is the midpoint of KF and KH ∥ EF Prove: HG ≅ EG.

What is the missing reason in the proof?

CPCTC

SAS

ASA

AAS

HL