Please I been struggling so much and need help please help me out and it is due today this geometry math assignment and I try and nothing. Works I need it by today and I willl mark

9a) corresponding

9b) Congruent

9c) x=5

10) x=4

11=9

Step-by-step explanation:

9a. The angles are corresponding, as, if you look at the 8 angles as 2 groups of 4, they would be in the same spot.

b. Corresponding angles are congruent (by corresponding angles are congruent theorem)

c. Because the angles are congruent, we know that

23x-5=21x+5

23x-21x=5+5

2x=10

x=5

10. We know that (see attached photo) angle a is equal to angle b through the vertical angle theorem. Then, we know that angle b is equal to angle c through corresponding angles. So, we know that a=b, and b=c, so through the  transitivity property, a=c, and c=90 degrees (it is a right angle)

Therefore, a=90 degrees

a=21x+6, so 21x+6=90

21x=84

x=4

11) This is almost the exact same problem as 10. We know that (see attached photo) a=b through vertical angles, and b=c through corresponding angles. Therefore, a=c

When you substitute the values of the two angles, we get:

-1+14x=12x+17

14x-12x=17+1

2x=18

x=9

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.