For each condition, listed below, right yes or no to predict whether you think the condition guarantees congruency for right triangles. 1) One leg congruent (L). 2) Both legs congruent (LL). 3) Hypotenuse congruent (H). 4) Hypotenuse and one leg congruent (HL). 5) One acute angle congruent (A). 6) one acute angle and one leg congruent (LA). 7) one acute angle and one hypotenuse congruent (HA).

To determine if the given conditions guarantee the congruency of right triangles, we can use the criteria for congruence specific to right triangles. The main criterion is the hypotenuse-Leg (HL) criterion, which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Here are the conditions with the congruence checks:

1. One leg congruent (L): No

- Knowing only one leg is insufficient to guarantee that the right triangles are congruent because the other leg and hypotenuse could differ.

2. Both legs congruent (LL): Yes

- If both legs of one right triangle are congruent to the corresponding legs of another right triangle, the triangles are congruent by the LL criterion (essentially SAS for right triangles).

3. Hypotenuse congruent (H): No

- Knowing only the hypotenuse is not sufficient to guarantee congruence because the legs' lengths could differ.

4. Hypotenuse and one leg congruent (HL): Yes

- This is a specific criterion for right triangles. If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent by the HL criterion.

5. One acute angle congruent (A): No

- Knowing only one acute angle is not enough to guarantee congruence because the lengths of the sides could vary.

6. One acute angle and one leg congruent (LA): Yes

- If one acute angle and the corresponding leg are congruent in two right triangles, the triangles are congruent by the ASA or AAS criterion applied to right triangles.

7. One acute angle and one hypotenuse congruent (HA): Yes

- If one acute angle and the hypotenuse are congruent in two right triangles, the triangles are congruent. This is because knowing the hypotenuse and an angle determines the triangle completely (by the AAS criterion applied to right triangles).

Therefore, the results are:

1. No

2. Yes

3. No

4. Yes

5. No

6. Yes

7. Yes