Triangle congruence by ASA and AAS Quiz Part 1
1. D. <MNP
2. C
3. HIJ = LKJ by ASA
1. Why did the angle go to the comedy club? Because it wanted to be acute triangle!
2. Why don't triangles go to parties? Because they always get obtuse!
3. Did you hear about the triangle that went on a diet? It lost some pounds and became congruent to another triangle by ASA!
To determine if the given triangles are congruent using ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side), we need to compare the corresponding angles and sides.
1. It seems that "<MNP" is mentioned, but it is not clear what is being compared to "<MNP" to determine congruence. To properly answer this question, please provide more information or context about the triangles and their corresponding parts.
2. The answer is "C". However, it is not clear what the question is regarding or what is being compared to determine congruence. If you can provide additional information or context, I can better assist you.
3. The statement "HIJ = LKJ by ASA" signifies that triangles HIJ and LKJ are congruent using the ASA (Angle-Side-Angle) congruence criterion. ASA states that if two triangles have two congruent angles and the included side (the side between the two angles) is congruent, then the triangles are congruent.
To verify this congruence using ASA, you would need to compare the angles and sides of the two triangles:
- First, check if angle HIJ is congruent to angle LKJ.
- Then, check if side HI is congruent to side LK.
- Lastly, check if angle JIH is congruent to angle JKL.
If all three pairs of corresponding angles and sides are congruent, then you can conclude that the triangles HIJ and LKJ are congruent by ASA.
1. The answer is D. △MNP. In order to prove triangle congruence using the ASA (Angle-Side-Angle) criterion, we need to show that two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle. Therefore, you should select the triangle that has <MNP as one of its angles.
2. The answer is C. The AAS (Angle-Angle-Side) criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent. So, in the context of the quiz, it is likely that this question is asking you to identify the triangle that satisfies the AAS criterion.
3. The information provided states that △HIJ is congruent to △LKJ by ASA. This means that the angle ∠HIJ is congruent to ∠LKJ, the angle ∠I is congruent to ∠L, and the side HI is congruent to LK. Therefore, you can conclude that △HIJ ≅ △LKJ based on the ASA congruence criterion.