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3 years ago

Given that ABCD is a parallelogram and AB is parallel to CD, which of the following statements is false? (1 point)

Mathematics

1 answer:

brilliants [131]3 years ago

5 0

Answer:

The correct option is;

Angle A and B are congruent

Step-by-step explanation:

The given parameters are;

Quadrilateral ABCD = Parallelogram

Side AB is parallel to CD

Therefore, we have for properties of a parallelogram

Opposite sides are parallel

Therefore, AB and CD are opposite sides

Opposite sides are congruent

Opposite angles are congruent, therefore ∠A and ∠C are congruent and ∠B and ∠D are congruent (depending on the orientation of side CD)

Consecutive angles are supplementary, therefore, ∠A and ∠B are supplementary angles and ∠C and ∠D are supplementary angles

Therefore, the statement which is false is Angle ∠A and ∠B are congruent.

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26. Define a relation ∼ ∼ on R 2 R2 by stating that ( a , b ) ∼ ( c , d ) (a,b)∼(c,d) if and only if a 2 + b 2 ≤ c 2 + d 2 . a2+

Tresset [83]

Answer:

~ is reflexive.

~ is asymmetric.

~ is transitive.

Step-by-step explanation:

~ is reflexive:

i.e., to prove $\forall (a, b) \in \mathbb{R}^2$ , $(a, b) R(a, b)$ .

That is, every element in the domain is related to itself.

The given relation is $\sim: (a,b) \sim (c, d) \iff a^2 + b^2 \leq c^2 + d^2$

Reflexive:

$(a, b) \sim (a, b)$ since $a^2 + b^2 = a^2 + b^2$

This is true for any pair of numbers in $\mathbb{R}^2$ . So, $\sim$ is reflexive.

Symmetry:

$\sim$ is symmetry iff whenever $(a, b) \sim (c, d)$ then $(c, d) \sim (a, b)$ .

Consider the following counter - example.

Let (a, b) = (2, 3) and (c, d) = (6, 3)

$a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13$

$c^2 + d^2 = 6^2 + 3^2 = 36 + 9 = 42$

Hence, $(a, b) \sim (c, d)$ since $a^2 + b^2 \leq c^2 + d^2$

Note that $c^2 + d^2 \nleq a^2 + b^2$

Hence, the given relation is not symmetric.

Transitive:

$\sim$ is transitive iff whenever $(a, b) \sim (c, d) \hspace{2mm} \& \hspace{2mm} (c, d) \sim (e, f)$ then $(a, b) \sim (e, f)$

To prove transitivity let us assume $(a, b) \sim (c, d)$ and $(c, d) \sim (e, f)$ .

We have to show $(a, b) \sim (e, f)$

Since $(a, b) \sim (c, d)$ we have: $a^2 + b^2 \leq c^2 + d^2$

Since $(c, d) \sim (e, f)$ we have: $c^2 + d^2 \leq e^2 + f^2$

Combining both the inequalities we get:

$a^2 + b^2 \leq c^2 + d^2 \leq e^2 + f^2$

Therefore, we get: $a^2 + b^2 \leq e^2 + f^2$

Therefore, $\sim$ is transitive.

Hence, proved.

3 0

3 years ago

Luke is building a bike ramp. The ramp is going to be 3 feet tall on the high end and 6 feet long. How long is the base of the r

eimsori [14]

Answer: 5.1961

Step-by-step explanation: I believe you would use the Pythagorean’s theorem, since it’s a problem about a ramp, always draw pictures for word problems. So you would plug your numbers in the formula and solve. 3 squared plus B squared (that’s what we are trying to find so its a variable) equals 6 squared. Then you square and it becomes 9 + b2= 36, subtract 9 on both sides, b2=27, then square root on both sides to get 5.1961. Hopefully that’s right. :)

7 0

4 years ago

Write what the expressions below best represent within the context of the word problem.

malfutka [58]

The answer to this is 2 nickles and 6 quarters

5 0

3 years ago

It costs $7.75 to enter an arcade and $0.25 to play an arcade game. You have $8.25. Write an

Sonbull [250]

Answer:

0.25g+7.75 less or equal to 8.25

Step-by-step explanation: