Question

proving congruent triangles with properties of trapezoids
given: isosceles trapezoid efgh
prove: \\( \triangle fhe \cong \triangle geh \\)
it is given that trapezoid efgh is an isosceles
trapezoid. we know that \\( \overline { fe } \cong \overline { gh } \\) by the definition of
. the base angle theorem of
isosceles trapezoids verifies that angle is
congruent to angle. we also see that \\( \overline { eh } \cong \overline { eh } \\)
by the property. therefore, by
we see that \\( \triangle fhe \cong \triangle geh \\).

Explanation:

• For the first blank: In an isosceles trapezoid, the non - parallel sides (legs) are congruent. So, by the definition of an isosceles trapezoid, \(FE\cong GH\).
• For the second and third blanks: The base - angle theorem of isosceles trapezoids states that base angles are congruent. In trapezoid \(EFGH\) with bases \(FG\) and \(EH\), \(\angle FEH\) and \(\angle GHE\) are base angles.
• For the fourth blank: \(EH\cong EH\) by the reflexive property (a segment is congruent to itself).
• For the fifth blank: We have two sides and the included angle ( \(FE\cong GH\), \(\angle FEH\cong\angle GHE\), \(EH\cong EH\)) congruent. So, by the Side - Angle - Side (SAS) congruence criterion, \(\triangle FHE\cong\triangle GEH\).

Answer:

1. isosceles trapezoid
2. \(\angle FEH\)
3. \(\angle GHE\)
4. reflexive
5. SAS