so there's a picture of one big triangle split right down the middle to make two smaller triangles with one small singer line going through the far left of the left triangle and a small singular going through the far right of the right triangle, F is the far left bottom corner G is at the top H is at the far right bottom angle and I is the line separating the two triangles.

Question

based on the labeled sides, state the postulate or theorem that can be used to conclude that the triangle are congruent.
A. SSS
B. SAS
C. ASA
D. AAS
E. HL

Answer 1

To determine which postulate or theorem can be used to conclude that the two triangles are congruent, we need to analyze the given information:

• F is the far left bottom corner of the left triangle.
• G is at the top of the big triangle.
• H is at the far right bottom angle of the right triangle.
• I is the line separating the two triangles.

From the description, it sounds like the two triangles share a common side (the line I) and they have corresponding sides at the bottom (FG and HI) that are equal because they are parts of the same larger triangle.

Given this setup, you can conclude that the triangles are congruent by using the SAS (Side-Angle-Side) postulate because:

1. You have a pair of corresponding sides (the segments from the bottom corners to the line I).
2. You have the angle at the top (the angle at G) which is common to both triangles due to the line separating them.

Therefore, the answer is B. SAS.

Answer 2

Can you explain what SSS,SAS, ASA, AAS, and HL mean, and dumb it way down please

Answer 3

Sure! Here’s a simple explanation of each acronym used for triangle congruence:

1. SSS (Side-Side-Side): If you know all three sides of one triangle are the same length as the three sides of another triangle, the triangles are congruent. Imagine two triangles where every side is the same length; they are the same shape and size!

2. SAS (Side-Angle-Side): If you know two sides of one triangle are the same length as two sides of another triangle and the angle between those two sides is the same, the triangles are congruent. Think of it like two triangles that “hug” one corner; if the lengths of their arms and the angle they form are the same, they are identical!

3. ASA (Angle-Side-Angle): If you know two angles and the side between them (the "corner side") in one triangle are the same as those in another triangle, the triangles are congruent. Picture two triangles that both have a pointy top and the same width; they must be the same height!

4. AAS (Angle-Angle-Side): If you know two angles in one triangle are the same as two angles in another triangle and one side that is not between the angles is the same, the triangles are congruent. Think of two triangles that both have the same two pointy corners and one matching leg; they must be the same shape!

5. HL (Hypotenuse-Leg): This one is special for right triangles. If you know the hypotenuse (the longest side opposite the right angle) and one leg (one of the other two sides) of one right triangle are the same as in another right triangle, they are congruent. Imagine a ladder as the hypotenuse and two equally long sides; if both triangles match up with a ladder and one leg, they're identical!

In summary:

• SSS: All sides match.
• SAS: Two sides and the angle between them match.
• ASA: Two angles and the side between them match.
• AAS: Two angles and a side (not in between) match.
• HL: Only for right triangles; the longest side and one leg match.

These are ways to prove that two triangles are exactly the same in size and shape!