select the correct answer from each drop-down menu.

if drop-down menu, then $\delta abc$ and $\delta efd$ are congruent by the asa criterion.
if drop-down menu, then $\delta abc$ and $\delta efd$ are congruent by the sas criterion.

Question

select the correct answer from each drop-down menu.

if drop-down menu, then $\delta abc$ and $\delta efd$ are congruent by the asa criterion.
if drop-down menu, then $\delta abc$ and $\delta efd$ are congruent by the sas criterion.

Accepted Answer

# Explanation:

⚡ Using what you learned: properties of triangles

## Step 1: Analyze the given markings

From the figure, we have the following marked congruent parts between $\Delta ABC$ and $\Delta EFD$:
- Side $AC \cong ED$ (indicated by the single tick mark on each segment).
- Angle $C \cong D$ (indicated by the triple arc mark on each angle).

## Step 2: Determine the condition for ASA congruence

The Angle-Side-Angle (ASA) criterion requires two angles and the included side of one triangle to be congruent to two angles and the included side of another triangle.

- The known congruent side is $AC$ in $\Delta ABC$ and $ED$ in $\Delta EFD$.
- The known congruent angle adjacent to this side is $\angle C$ in $\Delta ABC$ and $\angle D$ in $\Delta EFD$.
- To make the side the *included* side between two angles, we need the other adjacent angle to each side to be congruent:
  $$
  \angle A \cong \angle E
  $$

Thus, if **angle A is congruent to angle E**, then $\Delta ABC \cong \Delta EFD$ by the ASA criterion.

## Step 3: Determine the condition for SAS congruence

The Side-Angle-Side (SAS) criterion requires two sides and the included angle of one triangle to be congruent to two sides and the included angle of another triangle.

- The known congruent angle is $\angle C$ in $\Delta ABC$ and $\angle D$ in $\Delta EFD$.
- The known congruent side adjacent to this angle is $AC$ in $\Delta ABC$ and $ED$ in $\Delta EFD$.
- To make the angle the *included* angle between two sides, we need the other adjacent side to each angle to be congruent:
  $$
  BC \cong FD
  $$

Thus, if **side BC is congruent to side FD**, then $\Delta ABC \cong \Delta EFD$ by the SAS criterion.

# Answer:

- First drop-down: **angle A is congruent to angle E**
- Second drop-down: **side BC is congruent to side FD**

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QUESTION IMAGE

Question

Explanation:

Step 1: Analyze the given markings

Step 2: Determine the condition for ASA congruence

Step 3: Determine the condition for SAS congruence

Answer: