Question

1. elena needs to prove angles bed and bca are congruent. provide reasons to support each of her statements.

a. line m is parallel to line l.
b. angles bed and bca are congruent.
(from unit 1, lesson 20.)

1. triangle fgh is the image of isosceles triangle feh after a reflection across line hf. select all the statements that are a result of corresponding parts of congruent triangles being congruent.

a. efgh is a rectangle.
b. efgh is a rhombus.
c. diagonal fh bisects angles efg and ehg.
d. diagonal fh is perpendicular to side fe.
e. angle ehf is congruent to angle fgh.
f. angle feh is congruent to angle fgh.
(from unit 2, lesson 1.)

Explanation:

Question 5

Step1: Given information

This is the starting point of the proof.

Step2: Corresponding angles postulate

Since line \(m\) is parallel to line \(l\) (given in part a), and \(BC\) is a transversal, by the corresponding angles postulate, \(\angle BED\) and \(\angle BCA\) are congruent (part b).

• Option A:

A rectangle has four right - angles. There is no information given that the angles of \(EFGH\) are right - angles. So, \(EFGH\) is not necessarily a rectangle.

• Option B:

Since \(\triangle FEH\) is isosceles (\(EH = EF\)) and \(\triangle FGH\) is the reflection of \(\triangle FEH\) across \(HF\), then \(EH=EF = FG=GH\). A quadrilateral with all sides equal is a rhombus.

• Option C:

Because \(\triangle FEH\cong\triangle FGH\) (by reflection, which is a rigid transformation), \(\angle EFH=\angle GFH\) and \(\angle EHF=\angle GHF\). So, diagonal \(FH\) bisects \(\angle EFG\) and \(\angle EHG\).

• Option D:

There is no information to suggest that \(\angle EFH = 90^{\circ}\), so diagonal \(FH\) is not necessarily perpendicular to side \(FE\).

• Option E:

Since \(\triangle FEH\cong\triangle FGH\), \(\angle EHF\cong\angle FGH\) (corresponding parts of congruent triangles).

• Option F:

\(\angle FEH\) and \(\angle FGH\) are not corresponding angles of the congruent triangles \(\triangle FEH\) and \(\triangle FGH\).

Answer:

For part a, the reason is "Given". For part b, the reason is "Corresponding angles postulate (when two parallel lines are cut by a transversal, corresponding angles are congruent)".

Question 6