Question

PLEASE HELP ME!!! I WILL GIVE ALL THESE POINTS

Answer 1

Answer and Explanation to questions 13,14,15

13) $\mathbf{\overline{XY}\cong\overline{CD}}$        as given in the question.

14) $\mathbf{\overline{XY}\cong\overline{YZ}}$          Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.

15) $\mathbf{\overline{CD}\cong\overline{YZ}}$

$\because\overline{\textrm{XY}}\cong\overline{\textrm{CD}}$ and $\overline{\textrm{XY}}\cong\overline{\textrm{YZ}}$ . So, $\overline{\textrm{CD}}\cong\overline{\textrm{YZ}}$

Answer and Explanation to questions 16,17,18

∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°

And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.

∠3 + ∠1 = 180°    .............(i)

∠1 + ∠2 = 180°    .............(ii)

subtracting equation (i) and (ii) will give ∠3 = ∠2   ..........(iii)

15) ∠3 is supplementary to ∠1                        as given in the question

16) ∠2 is supplementary to ∠1                        as shown be equation (ii)

18) ∠3 ≅ ∠2                                                      as shown by equation (iii)

Answer and Explanation to questions 19

∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180°   .......(i)

∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180°   .......(ii)

subtracting equation (i) and (ii)

∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)

∠3 + ∠4 - ∠4 - ∠5 = 180°-180°

∠3 - ∠5 = 0

∴ ∠3 = ∠5     (Hence Proved)