A. What are the coordinates of the vertices of the triangle below? B. Find each side length.
C. Classify the figure. Use coordinate geometry (i. e. Pythagorean Theorem, distance formula,
slope formula, etc.) and properties of triangles to justify your response.

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length

now

AB:=units

BC:=units

AC:=units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

()²=2p²

16*5=2*()²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

Step-by-step explanation:

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length \sqrt{(x2-x1)²+(y2-y1)²}

(x2−x1)²+(y2−y1)²

now

AB:\sqrt{(-2-0)²+(3+3)²}

(−2−0)²+(3+3)²

=2\sqrt{10}2

10

units

BC:\sqrt{(0-4)²+(-3-5)²}

(0−4)²+(−3−5)²

=4\sqrt{5}4

5

units

AC:\sqrt{(-2-4)²+(3-5)²}

(−2−4)²+(3−5)²

=2\sqrt{10}2

10

units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

(4\sqrt{5}4

5

)²=2p²

16*5=2*(2\sqrt{10}2

10

)²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation:

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