Question

triangle jkl and triangle yza are shown. not drawn to scale. consider these triangles. not drawn to scale. which triangle is congruent to each triangle shown? △jkl≅△ blank △yza≅△ blank

Explanation:

Step1: Analyze $\triangle{JKL}$

In $\triangle{JKL}$, $\angle{L} = 90^{\circ}$, $\angle{K}=45^{\circ}$, $\angle{J}=45^{\circ}$, and $JL = LK = 1$, $JK=\sqrt{2}$ (by Pythagorean theorem $a^{2}+b^{2}=c^{2}$, here $a = b=1$, so $c=\sqrt{1^{2}+1^{2}}=\sqrt{2}$). Triangles with angles $45 - 45-90$ have side - length ratios of $1:1:\sqrt{2}$. The triangle $\triangle{OMN}$ has $\angle{N}=90^{\circ}$, $\angle{O} = 45^{\circ}$, $\angle{M}=45^{\circ}$, $ON=MN = 1$, $OM=\sqrt{2}$. So $\triangle{JKL}\cong\triangle{OMN}$ by Angle - Side - Angle (ASA) or Side - Angle - Side (SAS) or Hypotenuse - Leg (HL) congruence criteria (since the angles and side lengths match).

Step2: Analyze $\triangle{YZA}$

In $\triangle{YZA}$, $\angle{A}=106^{\circ}$, $\angle{Y}=\angle{Z}=37^{\circ}$, $YA = ZA = 5$, $YZ = 8$. The triangle $\triangle{VXW}$ has $\angle{X}=106^{\circ}$, $\angle{V}=\angle{W}=37^{\circ}$, $VX = WX = 5$, $VW = 8$. So $\triangle{YZA}\cong\triangle{VXW}$ by ASA or SAS congruence criteria (because the angles and side - lengths match).

Answer:

$\triangle{JKL}\cong\triangle{OMN}$
$\triangle{YZA}\cong\triangle{VXW}$