Question

question 23
with the following given in the drawings, which pair of triangles can be proven congruent by the side-angle-side postulate?
a
b
c
d

Explanation:

Analyze the SAS Congruence Postulate

Using the Triangle Congruence knowledge point
The Side-Angle-Side (SAS) postulate requires two pairs of congruent sides and a congruent included angle (the angle located directly between the two congruent sides).

Evaluate Option A

Using the Triangle Congruence knowledge point

• Two pairs of congruent sides are marked.
• The vertical angles between the intersecting lines are congruent.
• The congruent angle is not the included angle between the marked sides.
• Thus, SAS does not apply.

Evaluate Option B

Using the Triangle Congruence knowledge point

• Two pairs of congruent angles are marked.
• The shared vertical segment is congruent to itself.
• This represents an Angle-Angle-Side (AAS) scenario.
• Thus, SAS does not apply.

Evaluate Option C

Using the Triangle Congruence knowledge point

• Two pairs of congruent sides are marked.
• The shared vertical segment is congruent to itself by the reflexive property.
• This provides three pairs of congruent sides (SSS).
• Thus, SAS is not the primary postulate used.

Evaluate Option D

Using the Triangle Congruence knowledge point

• Two pairs of congruent sides are marked.
• One pair of congruent angles is marked.
• The marked angle is located directly between the two marked sides in both triangles.
• Thus, SAS applies.

Answer:

• a
• b
• c
• d (Correct answer)