Question

8)astional information is required in order to know that the triangles are congruenton given.10) asa11) aas12) sss© 2026 kuta software llc. all rights reserved

Explanation:

10) Step1: Identify given ASA components

We know $\overline{AB} \cong \overline{DB}$ (marked sides), $\angle ABC \cong \angle DBF$ (vertical angles). For ASA, we need a pair of adjacent angles.
Step2: Pick required congruent angles
We need $\angle A \cong \angle D$ (or $\angle C \cong \angle F$) to satisfy ASA (two angles and included side).

11) Step1: Identify given AAS components

We know $\overline{KT} \cong \overline{UT}$ (marked sides), $\angle KTM \cong \angle UTS$ (vertical angles). For AAS, we need one more non-included angle.
Step2: Pick required congruent angles
We need $\angle M \cong \angle S$ (or $\angle K \cong \angle U$) to satisfy AAS (two angles and non-included side).

12) Step1: Identify given SSS components

We know $\overline{ML} \cong \overline{TV}$, $\overline{KL} \cong \overline{UV}$ (marked sides). For SSS, we need the third pair of sides.
Step2: Pick required congruent sides
We need $\overline{MK} \cong \overline{TU}$ to satisfy SSS (three pairs of congruent sides).

11) (Second pair) Step1: Identify given AAS components

We know $\overline{ES} \cong \overline{TS}$ (marked sides), $\angle D \cong \angle R$ (unmarked, for AAS we need angles).
Step2: Pick required congruent angles
We need $\angle E \cong \angle T$ (or $\angle F \cong \angle R$) to satisfy AAS (two angles and non-included side).

Answer:

1. $\boldsymbol{\angle A \cong \angle D}$ (or $\boldsymbol{\angle C \cong \angle F}$)
2. $\boldsymbol{\angle M \cong \angle S}$ (or $\boldsymbol{\angle K \cong \angle U}$; for the lower pair: $\boldsymbol{\angle E \cong \angle T}$ or $\boldsymbol{\angle F \cong \angle R}$)
3. $\boldsymbol{\overline{MK} \cong \overline{TU}}$