Answer:
The correct option is B.
Step-by-step explanation:
Given information: AB\parallel DCAB∥DC and BC\parallel ADBC∥AD .
Draw a diagonal AC.
In triangle BCA and DAC,
AC\cong ACAC≅AC (Reflexive Property of Equality)
\angle BAC\cong \angle DCA∠BAC≅∠DCA ( Alternate Interior Angles Theorem)
\angle BCA\cong \angle DAC∠BCA≅∠DAC ( Alternate Interior Angles Theorem)
The ASA (Angle-Side-Angle) postulate states that two triangles are congruent if two corresponding angles and the included side of are congruent.
By ASA postulate,
\triangle BCA\cong \triangle DAC△BCA≅△DAC
Therefore option B is correct
Answer:
60°
Step-by-step explanation:
Angle 1 is a vertical angle to 60° by the definition of a vertical angle.
Answer:
Please check the explanation below.
Step-by-step explanation:
Some of the properties are defined as:
- <em>Distributive property</em>
For example,
suppose a=3, b=4, c=5
3(4+5) = 3(4) + 3(5)
3(9) = 12+15
27 = 27
- <em>Subtraction property of Equality</em>
if (a=b), then a-c = b-c
For example,
suppose a=2, b=2, c=5
if a = b ⇒ 2 = 2
then a-c = b-c ⇒ 2-5 = 2- 5 ⇒ -3 = -3
- <em>Addition property of Equality</em>
if (a=b), then a+c = b+c
For example,
suppose a=2, b=2, c=5
if a = b ⇒ 2 = 2
then a+c = b+c ⇒ 2+3 = 2+3 ⇒ 5 = 5
- <em>Multiplicative property of Equality</em>
if (a=b), then a×c = b×c
For example,
suppose a=2, b=2, c=5
if a = b ⇒ 2 = 2
then a×c = b×c ⇒ 2×5 = 2 × 5 ⇒ 10 = 10
- <em>Division property of Equality</em>
if (a=b), then a÷c = b÷c
For example,
suppose a=2, b=2, c=5
if a = b ⇒ 2 = 2
then a÷c = b÷c ⇒ 2÷5 = 2 ÷ 3 ⇒ 2/5 = 2/5
Let us solve the given equation using the above properties.
7n-16=47 Given
7n-16+16=47+16 1) Addtion property of Equality ∵ if (a=b), then a+c = b+c
7n=63 2) simplify
n = 9 3) Division property of Equality ∵ if (a=b), then a÷c = b÷c
Convex Polygons

All of its angles are less than 180°.
All of the diagonals are internal.
Concave Polygons

At least one angle measures more than 180°.
At least one of the diagonals is outside the shape of the polygon.
Equilateral Polygons

All sides are equal.
Equiangular Polygons

All angles are equal.
Regular Polygons

They have equal angles and sides
Irregular Polygons
They do not have equal angles and sides.
Types of Polygons based on Number of Sides
Triangle

3 sides.
Quadrilateral

4 sides.
Pentagon

5 sides.
Hexagon

6 sides.
Heptagon

7 sides.
Octagon

8 sides.
Enneagon or Nonagon

9 sides.
Decagon

10 sides.
Hendecagon

11 sides.
Dodecagon

12 sides.
Tridecagon or triskaidecagon

13 sides.
Tetradecagon or tetrakaidecago

14 sides.
Pendedecagon

15 sides.
Hexdecagon

16 sides.
Heptdecagon

17 sides.
Octdecagon

18 sides.
Enneadecagon

19 sides.
Icosagon

20 sides.
