CA bisects angle BAD and CA bisects angle BCD. Prove ABC congruent to ADC

Answers

Answer 1

The triangles are then congruent according to the SAS congruence criteria for triangles.

What is congruence?

Congruent triangles are those with the same size and form. This signifies that the respective sides are equal, as are the corresponding angles. We can determine if two triangles are congruent without evaluating all of their sides and angles. The phrase "congruent" refers to having exactly the same form and dimension. Even if we flip, turn, or rotate the forms, the shape and size should remain the same. In terms of shape and size, the adjective "congruent" implies "absolutely equal." The forms remain equal even when we spin, flip, or rotate them. Draw two circles with the same radius, then cut them out and stack them on top of each other.

Here,

If I understood correctly, then first let's call the angle BAC = CAD = α. From the statement we have angle ABC = 90° (AB ⊥ BC) and also angle ADC = 90° (AD ⊥ DC).

Then we have: angle BCA = ACD = 90 - α

We the have that:

AC = AC (the triangles share this size)

angle BCA = ACD

angle BAC = CAD

Then the triangles are congruent due to SAS criterion of congruence for triangle.

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Related Questions

A Jar of Dill costs $7.64. A jar of dill contains 4 oz., and a cup of dill weighs 2 oz. How much will 1 tbsp cost

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Answer:

$0.27875 or $0.28 1 cup = 2 ounces Number of cups in 1 jar = 4 ounce

Step-by-step explanation:

please help ASAP. DUE IN AN HOUR

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According to the given statement the answer of angle A is [tex]\mathrm{m} \angle A=65^{\circ}[/tex].

What is the parallelogram?

A parallelogram with the opposing sides perpendicular is called a quadrilateral (and therefore opposite angles equal). A parallelogram among all right angles generally known as a rectangle, whereas a quadrilateral having equal angles is known as a rhombus.

Briefing:

[tex]\mathrm{m} \angle F G D=35^{\circ}\\\mathrm{m} \angle DFG=180^{\circ}-69^{\circ}\\\\[linear pair of angle]\\mathrm{m} \angle DFG=111^{\circ}\\\mathrm{m} \angle F DG=180^{\circ}-(35^{\circ}+111^{\circ})\\\\mathrm{m} \angle F DG=34^{\circ}[/tex]

because DC||AB, so

[tex]\mathrm{m} \angle BDC={m} \angle ABD=Alternate angle[/tex]

[tex]so, \mathrm{m} \angle ABD=34^{\circ}[/tex]

because the sum of interior angle of a triangle = 180

[tex]so, \mathrm{m} \angle A=180^{\circ}-(81^{\circ}+34^{\circ})\\ \mathrm{m} \angle A=65^{\circ}[/tex]

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Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept. A function, g, has a growth factor of 2, an a value of 1, and passes through (1,-2). x f(x) 0 2 1 0 2 -6 3 -24 , ,

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The y-intercepts of the functions are

Function h(x) = -1Function g(x) = -1Function f(x) = 2

How to determine the y-intercepts?

The complete question is added at the end of this solution as an attachment

As a general rule, the y-intercept is the point in an equation or a function where x = 0

Using the above as a guide, we have the following:

The y-intercept of function h(x) = -1The y-intercept of function f(x) = 2

For the function g(x), we have

g(x) = abˣ

Using the given points (1, -2) and the growth factor of 2, we have

g(x) = a(2)ˣ

This means that

a(2)¹ = -2

So, we have

2a = -2

a = -1

So, the equation is

g(x) = -1(2)ˣ

Set x = 0

g(0) = -1(2)⁰

g(0) = -1

So, the y-intercept of function g(x) = -1

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Consider the equations and graph below.

y = negative 3 (x minus 1). Y = negative 3 x minus 1

On a coordinate plane, 2 lines are parallel to each other.

Answers

The equations on the graph have no solution

How to determine the solution to the system

From the question, we have the following equations that can be used in our computation:

y = -3(x - 1)

y = -3x - 1

Also, we have:

The lines are parallel to each other.

As a general rule:

Parallel lines are lines that do not intersect and they have the same slope

Because the lines do not intersect, it means that the system do not have any solution

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