Question

mark the image to show that the triangles are congruent by hl (hypotenuse-leg) theorem.

Explanation:

Step1: Identify the Hypotenuse-Leg (HL) Criteria

The HL theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. First, we need to identify the right triangles. The middle line (the horizontal one) and the two slant lines form two right triangles, sharing the middle leg (the horizontal segment) as one leg, and the hypotenuses are the two slant sides.

Step2: Mark the Congruent Parts

• The middle segment (let's call it \( \overline{AB} \)) is common to both right triangles, so it is congruent to itself (Reflexive Property). So we mark \( \overline{AB} \) with a single tick mark on both triangles.
• The hypotenuses (the two slant sides, say \( \overline{AC} \) and \( \overline{AD} \)) should be marked as congruent. We can mark them with double tick marks (or the same number of tick marks) to indicate they are congruent. Also, the right angles are formed between the middle leg and the other legs (the vertical? No, wait, the middle line is horizontal, and the slant lines form right angles with the middle line? Wait, actually, the two triangles are right - angled at the point where the middle line meets the vertex. So the right angles are congruent (all right angles are congruent). So we mark the right angles with a right - angle symbol.

Answer:

To show the triangles are congruent by HL:

1. Mark the common leg (the middle horizontal segment) with one tick mark on both triangles.
2. Mark the two hypotenuses (the two slant sides) with the same number of tick marks (e.g., two tick marks) to show they are congruent.
3. Mark the right angles (at the vertex where the middle segment meets the slant sides) with the right - angle symbol.