Consider the incomplete table and function rule given below.

Determine if triangle ABC with coordinates A (0, 2), B (2, 5), and C (−1, 7) is an isosceles triangle. Use evidence to support y

kirill115 [55]

Answer:

The triangle ABC is an isosceles right triangle

Step-by-step explanation:

we have

The coordinates of triangle ABC are

A (0, 2), B (2, 5), and C (−1, 7)

we know that

An isosceles triangle has two equal sides and two equal internal angles

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

substitute in the formula

$d=\sqrt{(5-2)^{2}+(2-0)^{2}}$

$d=\sqrt{(3)^{2}+(2)^{2}}$

$dAB=\sqrt{13}\ units$

step 2

Find the distance BC

substitute in the formula

$d=\sqrt{(7-5)^{2}+(-1-2)^{2}}$

$d=\sqrt{(2)^{2}+(-3)^{2}}$

$dBC=\sqrt{13}\ units$

step 3

Find the distance AC

substitute in the formula

$d=\sqrt{(7-2)^{2}+(-1-0)^{2}}$

$d=\sqrt{(5)^{2}+(-1)^{2}}$

$dAC=\sqrt{26}\ units$

step 4

Compare the length sides

$dAB=\sqrt{13}\ units$

$dBC=\sqrt{13}\ units$

$dAC=\sqrt{26}\ units$

$dAB=dBC$

therefore

Is an isosceles triangle

Applying the Pythagoras Theorem

$(AC)^{2} =(AB)^{2}+(BC)^{2}$

substitute

$(\sqrt{26})^{2} =(\sqrt{13})^{2}+(\sqrt{13})^{2}$

$26=13+13$

$26=26$ -----> is true

therefore

Is an isosceles right triangle

8 0

3 years ago

14

andriy [413]

Answer:

alam ko sagot pero mataas lang

4 0

2 years ago

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Please help. What is the circumference of the circle? (X+4)^2+(y-5)^2=81

PIT_PIT [208]

the radius: r^2 = 81

r =9

c = 2*pi*r

= 2 * pi * 9

= 18 *pi

Answer: 18*pi or approximately 56.62

8 0

3 years ago

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Help asap I will give u huge amount of brainly points

Minchanka [31]

Answer:

$\boxed{\sf -\dfrac{5}{8}}$

Use BODMAS rule,

where:

brackets
order
division
multiplication
addition
subtraction

Given expression:

$\rightarrow \sf -\dfrac{1}{5} \times [\:4-14\times\left(\dfrac{1}{4} \right)^2]$

simplify exponent

$\rightarrow \sf -\dfrac{1}{5} \times [\:4-14\times\left(\dfrac{1}{16} \right)]$

$\rightarrow \sf -\dfrac{1}{5} \times [\:4-\(\dfrac{14}{16}]$

$\rightarrow \sf -\dfrac{1}{5} \times [\:4-\(\dfrac{7}{8}]$

$\rightarrow \sf -\dfrac{1}{5} \times [\:\dfrac{32}{8} -\(\dfrac{7}{8}]$

$\rightarrow \sf -\dfrac{1}{5} \times [\:\dfrac{25}{8}]$

multiply fractions

$\rightarrow \sf -\dfrac{25}{40}$

$\rightarrow \sf -\dfrac{5}{8}$

8 0

1 year ago

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Complete the proof given below.

allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS

Reasons:

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ABCD is a parallelogram ${}$ 1. Given

2. $\overline{AB}$ ≅ $\overline{DC}$ and $\overline{BC}$ ≅ $\overline{DA}$ ${}$ 2. Opposite sides of a parallelogram

3. $\overline{AC}$ ≅ $\overline{CA}$ ${}$ 3. Reflexive property of congruency

4. ΔABC ≅ ΔCDA ${}$ 4. SSS

The correct options are therefore;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

brainly.com/question/4218263

brainly.com/question/21390857

8 0

2 years ago