CPM Homework Help : CCG Problem 8-87

Callie started to prove that given the information in the diagram at right, then $\overline{AB} \cong \overline{CD}$ . Copy her flowchart below on your paper and help her by justifying each statement.

This flowchart has 6 bubbles. Bubble # 1 has an arrow, pointing down to bubble # 3. Bubble numbers 2, 3, and 4 have arrows, pointing down to bubble # 5. Bubble # 5 has an arrow, pointing down to bubble # 6.

	Bubble # 1 $\enclose{circle}{\; \\ \quad \overline{AD} \parallel \overline{CB} \quad \\}$
	$\Huge \downarrow$
Bubble # 2 $\enclose{circle}{\; \\ \quad \angle A \cong \angle C \quad \\}$	Bubble # 3 $\enclose{circle}{\; \\ \quad \angle ADB \cong \angle CBD \quad \\}$	Bubble # 4 $\enclose{circle}{\; \\ \quad \overline{BD} \cong \overline{DB} \quad \\}$
$\Huge \searrow$	$\Huge \downarrow$	$\Huge \swarrow$
	Bubble # 5 $\enclose{circle}{\; \\ \quad \Delta ADB \cong \Delta CBD \quad \\}$
	$\Huge \downarrow$
	Bubble # 6 $\enclose{circle}{\; \\ \quad \overline{AB} \cong \overline{CD} \quad \\}$

Answer 1:

Given in diagram.
Bubble #1

Answer 2:

Given in diagram.

Added: Bubble #2

Answer 3:

If lines are parallel, then alt int angles are $\cong$ .

Added: Bubble #3

Answer 4:

Shared side (or Reflexive Property)

Added: Bubble #4

Answer 5:

$\text{AAS}\cong$

Added: Bubble #5

Answer 6:

Congruent triangles have congruent parts.

Added: Bubble #6

2 triangles share a horizontal side, the angles opposite the horizontal side, each have 1 tick mark, the left side of the top triangle, & right side of bottom triangle, each have 2 arrows.