Which Sentence is true?

The distance between the points (-2, -4) and (3,8) is?

forsale [732]

Answer:

(5,4)

Step-by-step explanation:

6 0

3 years ago

Which of the following is not part of the Triangle Proportionality Theorem?

natka813 [3]

Answer:

A. AA Similarity Theorem . True

B. Two sides divided proportionally. True

C. A parallel line to one side of a triangle. True

D. A perpendicular line to one side of a triangle. False

Step-by-step explanation:

The Triangle Proportionality Theorem says that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections.

Now, here the given statements are:

A. AA Similarity Theorem

TRUE, as the angles opposite to equal sides are equal.

And if lines are divided proportionally, both the triangles are Similar by AA similarity theorem.

B. Two sides divided proportionally.

TRUE,as the other two sides of the triangle are divided proportionally by the parallel line.

C. A parallel line to one side of a triangle.

TRUE, as the parallel line divides the other two non- parallel sides in equal proportions.

D. A perpendicular line to one side of a triangle.

FALSE, this part is not required anywhere in the given theorem result.

3 0

3 years ago

Select all the conditions for which it is possible to construct a triangle. (7.G.1.2) Group of answer choices a. A triangle with

saw5 [17]

Answer:

b, d, e, f

Step-by-step explanation:

Here are the applicable restrictions:

The sum of angles in a triangle is 180°, no more, no less.
The sum of the lengths of the two shortest sides exceeds the longest side.
When two sides and the angle opposite the shortest is given, the sine of the given angle must be at most the ratio of the shortest to longest sides.

a. A triangle with angle measures 60°, 80°, and 80° (angle sum ≠ 180°, not OK)

b. A triangle with side lengths 4 cm, 5 cm, and 6 cm (4+5 > 6, OK)

c. A triangle with side lengths 4 cm, 5 cm, and 15 cm (4+5 < 15, not OK)

d. A triangle with side lengths 4 cm, 5 cm, and a 50° angle across from the 4 cm side (sin(50°) ≈ 0.766 < 4/5, OK)

e. A triangle with angle measures 30° and 60°, and an included 3 cm side length (OK)

f. A triangle with angle measures 60°, 20°, and 100° (angle sum = 180°, OK)

_____

Additional comment

In choice "e", two angles and the side between them are specified. As long as the sum of the two angles is less than 180°, a triangle can be formed. The length of the side is immaterial with respect to whether a triangle can be made.

__

The congruence postulates for triangles are ...

SSS, SAS, ASA, AAS, and HL

These essentially tell you the side and angle specifications necessary to define a singular triangle. As we discussed above, the triangle inequality puts limits on the side lengths specified in SSS. The angle sum theorem puts limits on the angles when only two are specified (ASA, AAS).

In terms of sides and angles, the HL postulate is equivalent to an SSA theorem, where the angle is 90°. In that case, the angle is opposite the longest side (H). In general, SSA will specify a singular triangle when the angle is opposite the longest specified side, regardless of that angle's measure. However, when the angle is opposite the shortest specified side, the above-described ratio restriction holds. If the sine of the angle is less than the ratio of sides, then two possible triangles are specified.

4 0

3 years ago

(20 pts!) if the base of the roof has length 40 feet and x=30, which of the following gives the height of the roof?

musickatia [10]

Answer:

23.094 ft approximately

(If you want your answer in a different format, let me know please.)

Step-by-step explanation:

I would have solve this using tangent since the side opposite to x is asked for and the adjacent side to side is given as having a measurement of 40 ft.

But I think they want you to use the formula:

$l=\frac{b}{\cos(x)}$ .