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3 years ago

What additional information would you need to prove by the HL theorem?

Mathematics

1 answer:

Butoxors [25]3 years ago

8 0

Answer:

Answer: A $\overline{TM}\cong \overline{OR}$

Step-by-step explanation:

The HL Theorem states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Triangles TRO and OMT share the hypotenuse, so the first part of the theorem is met.

Both triangles are right because they have an internal angle of 90°, so the second condition is also met.

Since there is no indication of any leg to be congruent to another leg, we need additional information to prove that both triangles are congruent.

One of these two conditions should be met:

Side TM is congruent to side OR, or

Side MO is congruent to side RT.

From the available options, only the first is correct.

Answer: A $\mathbf{\overline{TM}\cong \overline{OR}}$

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3 years ago

How can you find the equation of a line that is parallel/perpendicular to a given line

alexdok [17]

In the Slope-Intercept Form, m is the slope and b is the y-intercept.

Finding The Equation of a Line Parallel to the Given Line: Let the given line be line a and the parallel line be line b.

1) Find the slope of line a.

Example: Line a --> $y = 5x + 2$ . The slope is 5.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of a point located on line b.

Example: The slope is 5 and the point is (2, 3), use the Slope-Intercept Formula, $y=mx+b$ ---> $3 = 5(2) + b$ . Then you solve for b.

$3 = 5(2) + b$

$3 = 10 + b$

$3 - 10 = 10 - 10 + b$

$-7 = b$ $b=-7$

The y-intercept of line b is -7

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is 5 and the y-intercept is -7. The equation of line b is $y = 5x - 7$ .

Finding The Equation of a Line Perpendicular to The Given Line: Let the given line be line a and the perpendicular line be line b.

1) Find the opposite reciprocal of the slope of line a.

Example: Line a --> $y=5x+2$ . The slope is 5, to find the opposite reciprocal of the slope you use n --> $-\frac{1}{n}$ . In this case, it would be $-\frac{1}{5}$ . The opposite reciprocal of the slope of line a is $-\frac{1}{5}$ , which would be the slope of line b.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of the point where line a and line b both intersect.

Example: The slope of line b is $-\frac{1}{5}$ and the point is (1, 7), use the Slope-Intercept Formula, $y=mx+b$ ---> $7=-\frac{1}{5}(1) + b$ . Then you solve for b.