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Answer 1

Step-by-step explanation:

Solutions:-

20)angle ABC = 85°

20)angle ABC = 85°21)BC = 16

Reason :-

From given triangles ,

Since ∆ ABC and ∆ DEF are congruent triangles

Congruent sides :-

AB = DE = 12

BC = EF = 16

AC = DF

and

Congruent angles :-

angle A = angle D = 50°

angle B = angle E = 85°

angle C = angle F= 45°

the sum of all angles in a triangle = 180°

=>50°+angle B +45° = 180°

=> angle B + 95°=180°

=> angle B = 180°-95°

=> angle B = 85°

angle B = angle E = 85°

22)AC = 18

Reason ;-

The perimeter is the sum of the lengths of the all sides

Given perimeter = 46

AB+BC+CA = 46

=> 12+16+AC = 46

=> 28+AC = 46

=>AC = 46-28

=> AC = 18 units

23)angle U = angle R

Reason:-

In the congruent triangles ∆SUM and ∆PRO

Corresponding angles are equal .They are

angle S = angle P

angle U = angle R

angle M = angle O

24)PQ

Reason :-

In ∆PQR , angle P and Angle Q are the adjacent angles with the common side PQ.

The included side of angle P and angle Q = PQ

25)AC = 8 units

Reason:-

Since ∆DEF and ∆ABC are congruent triangles

EF = AC = 8 units

26)By ASA Property the two triangles are congruent.

27)SSS triangle congruence property

28)AB= XZ

Reason:-

In ∆ABC and ∆XYZ ,

The corresponding sides AB and XY are eauql.

AB= XZ is not true

29)angle B.

Reason :-

The sides AB and BZ are having common vertex B.

So Included angle of AB and BZ is angle B.

30)BY SAS Property they are congruent triangles