Answer:
It is given that, AB and P Q are parallel lines.Line segment CR and D S, intersect the two lines.
Line segment CR and D S ,are Transversal to parallel lines, AB and P Q.
⇒∠C + ∠ R=180°
⇒90°+∠ R=180°
∠ R=180°-90°
∠R=90°
Similarly, ∠S=90°
→∠R+∠S=90°+90°=180°
As, sum of interior angles on the same side of transversal is 180°, so lines are Parallel.
→CR║DS
Also, AB║CD→CD║RS.
If in a Quadrilateral, opposite sides are parallel, then it is a Parallelogram,and also each interior angle has measure 90°, so it is a Rectangle.
In a rectangle opposite sides are equal.
Step-by-step explanation:
Answer:
k = -
Step-by-step explanation:
Given that x varies directly with y then the equation relating them is
x = ky ← k is the constant of variation
To find k use the condition x = - 3 when y = 12
- 3 = 12k ( divide both sides by 12 )
= k , that is
k = -
Hello!
Say that n is the number. There are two parts to this statement. The first part is "four less than three times a number", and the second is "is three more than two times the number. An expression fitting the first part will go on the left side of the equation, and the second part will go on the right.
Look at the first part. "Four less than three times a number". The first thing being done here is the <u>three times a number.</u> This would be 3n, as it is 3 times n. Now, there is the <u>four less</u> part. You would therefore have to subtract 4 from 3n, to get 3n - 4.
Now the second part. "Is three more than two times the number". The first thing being done here is the <u>two times the number</u>. That would be 2n. The next is "is three more than". If the other side is three more than 2n, then you must add 3 to 2n to make them equivalent. Therefore, it would be 2n + 3.
Now, set them equal to each other, and solve.
3n - 4 = 2n + 3
3n - 2n = 3 + 4
n = 7
Therefore, your number is 7.
Hope this helps!
Alternate interior angles theorem.
<u>Step-by-step explanation:</u>
By using the definition of Alternate Interior Angles theorem, we can say that If a transversal cuts any two parallel lines, then those pairs of alternate interior angles are seems to be congruent.
So in the given triangle,
∠4 ≅ ∠2
∠5 ≅ ∠3
Sum of all the angles in a triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Since from the above congruence, we can write that
∠1 + ∠4 + ∠5 = 180°
Hence proved.
Divide and simplify radical expressions that contain a single term.