Pls help me with this proof
#Can someone help me with number 8?
mighty ibex
violet wrenBOT
meager nova
Okay so
We are given that YX=ZX right?
So what type of triangle is YXZ?
Similarly, we are given that YO=ZO , so what type of triangle is YOZ?
meager nova
Yeah, and do you remember that an isosceles triangle has equal angles at its base?
Idk if you have to prove this as a step but
mighty ibex
Yeah, and do you remember that an isosceles triangle has equal angles at its bas...
That’s a new thing I learned lol
meager nova
If you draw the height of an isosceles triangle, then since AC=AB, AD=AD, and D is a right angle, you know that right triangles ACD and ABD are congruent, so the angles DCA and DBA are equal
So you're given that YXZ is isosceles and that YOZ is isosceles
So looking at YXZ, the entire angle at Y is equal to the entire angle at Z, so (1+2)=(3+4) right
And also from isosceles triangle YOZ, the angle at 2 is equal to the angle at 3
so (<1+<2)=(<3+<4)
and <2=<3
So what can u do to those equations to get <1=<4
mighty ibex
Subtraction property?
meager nova
Yea
mighty ibex
Can you check my proof when I am finished
meager nova
ye
meager nova
I think so if your teacher is fine with the the fact that isosceles means equal angles(proving this separately prob isn't necessary here)
mighty ibex
Would my next statement be <2=<3 because of the base angles of isosceles triangle are congruent?
meager nova
Yeah since OY,OZ= <2=<3
mighty ibex
Wait can I just skip that and write <1=<4 instead?
meager nova
Well how do you know that <1=<4 without subtracting the two equations
You prob need to justify why <2=<3
meager nova
Yeah that should work
On a side note you should look up Art of problem solving intro to geometry if u would like to get better at geo and find some very cool problems
mighty ibex
Ok thanks for the help
Can you also help with another problem? Its fine if you can't
meager nova
Yes
mighty ibex
Number 12
meager nova
AB=AC so what kind of triangle is ABC?
mighty ibex
Isosceles
meager nova
Alright so maybe we want to show that triangle AXB is congruent to triangle AYC. We have AB=AC, and are given that <1=<3. Do you see another pair of angles that you could show are equal for these two triangles to use ASA congruence?(Recall ASA means two triangles are congruent if two angles and the side between them are equal)
meager nova
Is it <B=<C?
Yes! Although make sure you see why we can't use <2 here. The triangles are AXB and AYC, and <2 is not an angle of either of these triangles
mighty ibex
Ohh
meager nova
AB=AC so what kind of triangle is ABC?
So if we want to show that <b=<c, how does this help with that?
mighty ibex
We can use the ASA congruence to say that triangle AXB is congruent to triangle AYC?
meager nova
We can use the ASA congruence to say that triangle AXB is congruent to triangle ...
Yeah, but to show that <b=<c, we use the fact that AB=AC from the isosceles fact is what i meant, but yeah ASA for these triangles is what i was hinting at
mighty ibex
Wait I'm still kind of confused why <B=<C
Can you explain a little bit more on that?
meager nova
So we are given that AB=AC right? Remember from the last problem that an isosceles triangle means that its base angles are equal?
meager nova
Idk if you have to prove this as a step but
from this
meager nova
yeah, you might want to include somewhere that you're using the fact that AB=AC, <b=<c, and <1=<3 for step 3, but this should work
Also finish the proof after step 3, we still need to show that ax=ay
mighty ibex
Is it AX=AY because corresponding parts of congruent triangles are congruent?
Sorry if I'm a bother
meager nova
u should check out this book also https://artofproblemsolving.com/store/book/intro-geometry
np bye
mighty ibex
Ok