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4 years ago

Given:

Mathematics

2 answers:

mart [117]4 years ago

6 0

Answer: The answer is ASA congruence rule.

Step-by-step explanation: We have the following rules for congruence of two triangles -

(i) SSS rule : If all the three sides of a triangle are equal to the corresponding three sides of the other triangle, then both of them are congruent by SSS rule.

(ii) ASA rule : If two angles and the side between them are equal to the corresponding two angles and the side between them of the other triangle, then the two triangles are congruent.

(iii) SAS rule : If two sides and the angle between them are equal to the corresponding two sides and the angle between them of the other triangle, then they are congruent.

Given that - In ΔABP and ΔCDQ (please the attached figure),

∠1 = ∠4,

∠2 = ∠3

and AB = CD.

Thus, ΔABP ≅ ΔCDQ by ASA rule.

Thus, the correct answer is ASA rule.

maxonik [38]4 years ago

3 0

The following triangle congruence theorems that would be used as proof is ASA

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A diver dives from the board at a local swimming pool. Her height, y, in metres, above the water in terms of her horizontal dist

Aneli [31]

Answer:

4 meters

Step-by-step explanation:

Given a quadratic equation in which the coefficient of $x^2$ is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

$y= -x^2 + 2x + 3$

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry, $x=-\dfrac{b}{2a}$

$x=-\dfrac{2}{2*-1}\\x=1$

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

$y(1)= -1^2 + 2(1) + 3=-1+2+3=4m$

The maximum height of the diver is therefore 4 meters.

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3 years ago

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3 years ago

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Lady bird [3.3K]

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3 years ago

HELP! Find the value of sin 0 if tan 0 = 4; 180 < 0< 270

BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

$\large \boxed{sin \theta = tan \theta cos \theta} \\ \large \boxed{tan^{2} \theta + 1 = {sec}^{2} \theta}$

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

$\large{ {4}^{2} + 1 = {sec}^{2} \theta } \\ \large{16 + 1 = {sec}^{2} \theta } \\ \large{ {sec}^{2} \theta = 17}$

As we know, sec²θ = 1/cos²θ.

$\large \boxed{sec \theta = \frac{1}{cos \theta} } \\ \large \boxed{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta} }$

And thus,

$\large{ {cos}^{2} \theta = \frac{1}{17}} \\ \large{cos \theta = \frac{ \sqrt{1} }{ \sqrt{17} } } \\ \large{cos \theta = \frac{1}{ \sqrt{17} } \longrightarrow \frac{ \sqrt{17} }{17} }$