Question

13
given:
\\( \overline { h a } \cong \overline { a s } \\)
\\( \overline { h s } \perp \overline { a m } \\)
\\( \delta h a m \cong \delta \\)____ by____

Explanation:

Step1: Identify right angles

Since $HS\perp AM$, $\angle HMA=\angle SMA = 90^{\circ}$ (Definition of perpendicular lines).

Step2: Identify hypotenuse and leg

We are given that $HA\cong AS$ (hypotenuse) and $AM$ is common to both $\triangle HAM$ and $\triangle SAM$ (leg).

Step3: Apply congruence criterion

In right - angled triangles $\triangle HAM$ and $\triangle SAM$, by the Hypotenuse - Leg ($HL$) congruence criterion for right - angled triangles, $\triangle HAM\cong\triangle SAM$.

Answer:

$\triangle HAM\cong\triangle SAM$ by $HL$ (Hypotenuse - Leg)