Question

which two triangles are congruent by the sas theorem? complete the congruence statement.

Explanation:

Step1: Recall SAS Congruence Rule

SAS requires 2 sides + included angle ≅.

Step2: Match sides/angle for $\triangle BCD$

In $\triangle BCD$: $\overline{BC}$ (1 tick), $\angle C$, $\overline{CD}$ (2 ticks)

Step3: Match sides/angle for $\triangle XYZ$

In $\triangle XYZ$: $\overline{XZ}$ (1 tick), $\angle X$, $\overline{XY}$ (2 ticks)

Step4: Match sides/angle for $\triangle RST$

In $\triangle RST$: $\overline{RS}$ (1 tick), $\angle R$, $\overline{RT}$ (2 ticks)

Step5: Identify congruent pairs

$\triangle BCD$ and $\triangle RST$ have matching 1-tick side, included angle, 2-tick side.

Answer:

$\triangle BCD \cong \triangle RST$