Line ST connects point S and point T
1 answer:
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Answer:
1. Perpendicular
2. Isosceles
3. Never
Step-by-step explanation:
1. AC ⊥ BD because diameter of a square are perpendicular bisector of each other.
2. In Δ AOB , By using pythagoras : AB² = OA² + OB² .......( 1 )
In Δ COB , By using pythagoras : BC² = OC² + OB² ..........( 2 )
But, OA = OC because both are radius of same circle
So, by using equations ( 1 ) and ( 2 ), We get AB = BC ≠ AC
⇒ ABC is a triangle having two equal sides so ABC is an isosceles triangle.
3. The side can never be equal to radius of circle because the side of the square will be chord for the circle and in a circle chord can never be equal to its radius
<h2>Answer and Explanation to questions 13,14,15</h2>
13) as given in the question.
14) Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.
15)
and
. So,
∠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)
<h2>Answer and Explanation to questions 19</h2>∠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)
Answer:
2(x-1)(x-4)
Step-by-step explanation:
Begin by dividing each term by 2 and pulling the 2 to the front.
This is a trinomial. Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as
.
a=1, c=4
ac=4 and add to b=-5 which -1 and -4 satisfy
The factored form is 2(x-1)(x-4).