Question

Given: EFGH is a rectangle

Prove: Segment FH is congruent to Segment GE

Answer 1

The blanks in the proof are

a. All rectangles are parallelogram

b. EF ≅ GH

c. Transitive property of equality

d. Vertex angle of rectangle are right angles

e. FEH ≅ GHE

f. SAS congruence theorem

g CPCTC

What is SAS congruence theorem

SAS congruence theorem states that: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

The included angle in this case is the right triangle.

CPCTC (Corresponding Parts of Congruent Triangles are Congruent): asserts that if two triangles are congruent, then their corresponding parts (angles and sides) are congruent.

hence we can say that: Segment FH is congruent to Segment GE

Answer 2

Explanation:

Statements Reasons

1). FGH is a rectangle 1). Given

2). EFGH is a parallelogram 2). a. All rectangles are parallelogram

3). EF ≅ b. GH 3). Opposite sides of a parallelogram are

equal in measure

4). EH ≅ EH 4). c. Reflexive property

5). ∠FEH and ∠GHE are the 5). d. Property of a rectangle

right angles

6). ∠FEH ≅ e. ∠GHE 6). Right angle theorem

7). ΔFEH ≅ ΔGHE 7). f. SAS postulate of congruence

8). FH ≅ GE 8). g. CPCTC (corresponding parts of

congruent triangles are congruent)