For the correspondence ABC leftrightarrow XYZ | vedclass

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Question

$(A)$ To determine the correct matching, we analyze the similarity criteria for triangles:$1.$ Given $\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \co

Vedclass · Accepted Answer

$1-b, 2-c, 3-a$

Vedclass · Answer

$(A)$ To determine the correct matching, we analyze the similarity criteria for triangles:$1.$ Given $\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$. This satisfies the $SAS$ (Side-Angle-Side) similarity criterion. Thus, $1-b$.$2.$ Given $\angle A \cong \angle X, \angle B \cong \angle Y$, and $\angle C \cong \angle Z$. This satisfies the $AAA$ (Angle-Angle-Angle) similarity criterion. Thus, $2-c$.$3.$ Given $\frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX}$. This satisfies the $SSS$ (Side-Side-Side) similarity criterion. Since $SSS$ is not listed as an option in Part $II$, this corresponds to $d$ (None of the conditions apply).Therefore, the correct matching is $1-b, 2-c, 3-d$.

Part $I$	Part $II$
$1.$ In $\Delta ABC$ and $\Delta XYZ, \frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$	$a. SSS$ condition
$2.$ In $\Delta ABC$ and $\Delta XYZ, \angle A \cong \angle X, \angle B \cong \angle Y$ and $\angle C \cong \angle Z$	$b. SAS$ condition
$3.$ In $\Delta ABC$ and $\Delta XYZ, \frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX}$	$c. AAA$ condition
-	$d. \text{None of the conditions apply}$

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