verify the asa postulate for triangle congruence by using congruence transformations.
given: $ \overline { e k } \cong \overline { l h } $
$ \angle e \cong \angle h $
$ \angle k \cong \angle l $
prove: $ \triangle e k s \cong \triangle h l a $
since $ \angle e \cong \angle h $, translate $ \triangle h l a $ so that points e and h coincide.
next rotate $ \triangle h l a $ so that side hl overlaps side ek.
since each vertex in $ \triangle h l a $ coincides with its corresponding vertex in the other triangle, there is a congruence transformation that maps $ \triangle h l a $ onto the other triangle, so $ \triangle h l a \cong \triangle \square $.

Question

Accepted Answer

# Explanation:
## Step1: Use congruence transformations
We are given $\angle E\cong\angle H$, $\overline{EK}\cong\overline{LH}$, and $\angle K\cong\angle L$. First, we translate $\triangle HLA$ so that point $E$ (from $\triangle EKS$) and point $H$ (from $\triangle HLA$) coincide because $\angle E\cong\angle H$.
## Step2: Rotate the triangle
Next, since $\overline{EK}\cong\overline{LH}$, we rotate $\triangle HLA$ so that side $HL$ (from $\triangle HLA$) overlaps side $EK$ (from $\triangle EKS$).
## Step3: Check vertex - to - vertex correspondence
After the translation and rotation,  each vertex in $\triangle HLA$ coincides with its corresponding vertex in $\triangle EKS$. By the definition of congruent triangles (if there is a congruence transformation that maps one triangle onto another, the two triangles are congruent), we can say that $\triangle HLA\cong\triangle EKS$

# Answer:
$\triangle EKS$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Use congruence transformations

Step2: Rotate the triangle

Step3: Check vertex - to - vertex correspondence

Answer: