Question

triangles
separating overlapping triangles and identifying common features
use the figure above to complete the following.
(a) $\triangle hil$ and $\triangle jik$ have been separated. fill in the missing vertex labels.
(b) choose the correct statement below about $\triangle hil$ and $\triangle jik$.
then fill in the additional information as necessary.
\bigcirc the triangles have a common side.
common side: (choose one)
\bigcirc the triangles have a common angle.
common angle: (choose one)
\bigcirc the triangles have neither a common side nor a common angle.

Explanation:

Step1: Match sides for ΔHIL

From the original figure, ΔHIL has side 10 and side 8 (implied, paired with vertex I). Label the triangle:

• Bottom vertex: $L$ (connected to side 10)
• Left vertex: $I$
• Top vertex: $H$
• Right vertex (bottom): $L$ (corrected: vertices are $I$, $L$, $H$: left = $I$, bottom = $L$, top = $H$)

Step2: Match sides for ΔJIK

From the original figure, ΔJIK has side 2 and side 9 (implied, paired with vertex K). Label the triangle:

• Top vertex: $K$
• Left vertex: $J$
• Bottom vertex: $I$

Step3: Identify common features

Compare ΔHIL ($I, H, L$) and ΔJIK ($J, I, K$): they share vertex $I$, so they share $\angle I$.

Answer:

(a)
Left triangle (ΔHIL):

• Left label: $I$
• Bottom label: $L$
• Top label: $H$

Right triangle (ΔJIK):

• Left label: $J$
• Top label: $K$
• Bottom label: $I$

(b)
The triangles have a common angle.
Common angle: $\angle I$ (or $\angle HIL = \angle JIK$)