Homework problems? I'll help you out

It's a triangle, with no present angle, which (for lower years of maths) has at least one side with a length.

Hypotenuse = longest side. Trying to find this is C squared = the square root of bracket A squared + B squared bracket [That's what you put in a calculator]. So, X = the square root of bracket 15 squared + 20 squared bracket.
Windows calculator says the answer is 25, which would make it certain type of triangle (the most famous being one that has side lengths of 3, 4 and 5).

If trying to find the shorter sides, however, you use A squared = the square root of bracket C squared - B squared bracket.
A = X, B = 15 and C = 20.
X = the square root of bracket 20 squared - 15 squared bracket.

 

Okay then how do I prove two triangles are similar using angle-angle postulate?

 

I would ask for you to tell me Pi, but...

 

If two pairs of corresponding angles were already proven congruent, then the third pair is automatically congruent.
Ex:
Given: Triangle ABC; Angle A = 67 degrees, Angle B = 37 degrees; Triangle XYZ; Angle X = 67 degrees, Angle Y = 37 degrees
Prove: Triangle ABC ~ Triangle XYZ
The sum of the three angles in a triangle is equal to 180 degrees no matter what, so, solving for Angle C, 67 + 37 = 104, 180 - 104 = 76 and, solving for Angle Z, 67 + 37 = 104, 180 - 104 = 76 which proves Angle C and Angle Z are congruent.

If three pairs of corresponding angles are congruent, the pair of triangles is similar. The sides must be taken into account in order to prove that the pair is congruent, though.

 

HOW DO YOU PROVE VERTICAL ANGLES
I HATE GEOMETRY PROOFS
WAAAA

 

Vertical Angles? If two lines intersect, the opposite angles are congruent.
Here, Angle 1 is congruent to Angle 3, and Angle 2 is congruent to Angle 4.

 

Nono like statements and reasons.
Like in a T chart.
Here something like this:

Just with the vertical angles stuff and reasons.

 

Does this make sense. Or nah

 

Ok. To put a reason for two angles created by intersecting lines, you could just put vertical angles or Line ___ intersects Line ___ thus creating vertical angles. For that attachment, did you want an explanation as to which postulates and theorems to put in for each reason?

 

This absolutely makes sense.