All right...before we begin, let's lay some ground rules about the postulate your teacher asks for in every problem. <em>If you already know what they are, skip this paragraph...</em>
A postulate is a statement that claims how the triangles are congruent from looking at the paper. For example, on number 2 we have three sides of the triangle so we would use the postulate SSS (side, side, side). However, number one we would use SAS (side, angle, side) because we see the angle square showing it is a 90-degree angle.
Let's begin! (I haven't done triangles in a while so I apologize in advance if some of my answers might be incorrect on the congruent (yes or no) part of it.)
1.
A) From a visual perspective, we can see the triangles are congruent.
B) ABE = CDE because they are the corresponding points.
C) We can use SAS for the postulate.
2.
A) Yes, they are congruent.
B) OLE = OVE
C) We can use SSS for their postulate.
3.
A) Yes, they are congruent.
B) AWT = ERT
C) We can use SAS for the postulate.
4.
A) I believe the triangles are congruent. You might want to check me on that.
B) GFE = FGH
C) SSS
5.
A) They are congruent because if IH bisects it, it is directly in the middle. So, we know that WH = HS and IH = IH (duh.) and their angles match.
B) WHI = SHI
C) SAS
6.
A) This one is intriguing because it would state above the shape "LE bisects LGUE." I'm going to take that it isn't exactly in the middle, but I am still going to say it is congruent.
B) LGE = EUL
C) ASA
7.
A) Yes, they are definitely congruent.
B) RTU = TRS
C) SSS (We have nothing that indicates angles.)
8.
A) Yes, they are congruent.
B) YWV = VZY
C) We can use SAS. (Might want to check that one.)
9.
A) I would say this one is NOT congruent.
B) There are only two points. One way is HT = MA
C) They are not congruent, you can not use a postulate. However, if you teacher insists on putting one, I would use SAS.
Once again, I would be careful about my answers. I haven't worked with triangles in a few years. If my math is incorrect, or I didn't give the answer you were looking for, please let me know. However, if my math is on point, please consider marking as <em>Brainliest</em>.
Have a good one.
God Bless.
Answer:
B, D, and E.
Inequalities are recognized from >, <, ≤, and ≥ signs.
I uploaded the answer to a file hosting. Here's link:
bit.
ly/3a8Nt8n
Side of the original square is 5 cm.
Step-by-step explanation:
- Step 1: Let the side of the original square be x. Then side of the new square = x + 3 and Area of new square = 64 cm²
Area of a square = (side)²
⇒ 64 = (x + 3)²
⇒ 64 = x² + 6x + 9
⇒ x² + 6x - 55 = 0
⇒ x² + 11x - 5x - 55 = 0 (Since 6x = 11x - 5x as part of factorizing)
⇒ x(x + 11) - 5(x + 11) = 0
⇒ (x + 11)(x - 5) = 0
⇒ x = -11 and x = 5 (Lengths can't be negative)
Side of the original square is 5 cm.
