Question

logo designs in the design shown, $\triangle abi \cong \triangle ebf$ and $\triangle cbd \cong \triangle hbg$.
name the congruent angles and congruent sides of a pair of congruent triangles.
$\triangle abi \cong \triangle \boldsymbol{\text{select choice}}$ $\triangle cbd \cong \triangle \boldsymbol{\text{select choice}}$
$\angle a \cong \angle \boldsymbol{\text{select choice}}$
$\angle abi \cong \angle \boldsymbol{\text{select choice}}$
$\angle i \cong \angle \boldsymbol{\text{select choice}}$
segment $ab \cong$ segment $\boldsymbol{\text{select choice}}$
segment $bi \cong$ segment $\boldsymbol{\text{select choice}}$
segment $ai \cong$ segment $\boldsymbol{\text{select choice}}$

Explanation:

Step1: Analyze $\triangle ABI \cong \triangle EBF$

When two triangles are congruent, their corresponding vertices are in order. Given $\triangle ABI \cong \triangle EBF$, the corresponding angles and sides are determined by the order of the vertices.

• Corresponding angles: $\angle A$ corresponds to $\angle E$, $\angle ABI$ corresponds to $\angle EBF$, $\angle I$ corresponds to $\angle F$.
• Corresponding sides: Segment $AB$ corresponds to segment $EB$, segment $BI$ corresponds to segment $BF$, segment $AI$ corresponds to segment $EF$.

Step2: Analyze $\triangle CBD \cong \triangle HBG$

For $\triangle CBD \cong \triangle HBG$, using the order of vertices:

• Corresponding angles (though not fully asked here, for the congruent triangle pair, the second triangle is $\triangle HBG$).
• Corresponding sides would follow the vertex order.

Answer:

For $\triangle ABI \cong \triangle \boldsymbol{EBF}$ and $\triangle CBD \cong \triangle \boldsymbol{HBG}$:

• $\angle A \cong \angle E$
• $\angle ABI \cong \angle EBF$
• $\angle I \cong \angle F$
• Segment $AB \cong$ Segment $EB$
• Segment $BI \cong$ Segment $BF$
• Segment $AI \cong$ Segment $EF$

(Note: The dropdowns should be filled as: $\triangle ABI \cong \triangle EBF$, $\triangle CBD \cong \triangle HBG$, $\angle A \cong \angle E$, $\angle ABI \cong \angle EBF$, $\angle I \cong \angle F$, Segment $AB \cong$ Segment $EB$, Segment $BI \cong$ Segment $BF$, Segment $AI \cong$ Segment $EF$)