Question

1. a partially completed chart shows the hierarchy of a set of polygons.

move a term to each blank box to complete the chart.
kite parallelogram rectangle rhombus square

1. two parallel lines, a and b, are cut by a transversal c as shown.

drag a statement or reason to each blank in the table to complete the proof that ∠1 ≅ ∠7
corresponding angles formed by parallel lines are congruent
alternate interior angles formed by parallel lines are congruent
alternate exterior angles formed by parallel lines are congruent

Explanation:

Step1: Fill polygon hierarchy blanks

1. Parallelogram
2. Rectangle
3. Rhombus
4. Square

(Note: Kite is a non-parallelogram quadrilateral, so it does not fit in this parallelogram-focused hierarchy.)

Step2: Complete angle proof steps

Step2a: State vertical angle congruence

Statement 2: $\angle 1 \cong \angle 3$
Reason 2: Vertical angles are congruent

Step2b: State parallel line angle congruence

Statement 3: $\angle 3 \cong \angle 7$
Reason 3: Corresponding angles formed by parallel lines are congruent

Step2c: Apply transitive property

Reason 4: Transitive property

Answer:

1. Polygon Hierarchy Completion:
2. Parallelogram
3. Rectangle
4. Rhombus
5. Square

1. Angle Proof Completion:

Statements	Reasons
2. $\angle 1 \cong \angle 3$	2. Vertical angles are congruent
3. $\angle 3 \cong \angle 7$	3. Corresponding angles formed by parallel lines are congruent
4. $\angle 1 \cong \angle 7$	4. Transitive property