Geometry - Unit 5 Review
A right triangle has a hypotenuse whose length is 26 inches and a leg whose length is 10 inches. What is the area of the right triangle in square inches?
A = 120 sq. inches
An equilateral triangle has a side length of 10 inches. What is the area of the triangle in simplest radical form?
A = 25√3
Two line segments, AB and CD, have endpoints at A(-5, 11), B(3, 5), C(9, 3), and D(2, 10). Which of the two line segments is longer? Show evidence to support your claim.
AB is longer! AB = 10 or √100 CD = √99
Find the coordinates of B if M (-1, 3) is the midpoint of AB and A has the coordinates (5, 6).
B (-7, 0)
Solve for the missing side of a right triangle if... A = 4 B = ? C = 8
b = 4√3
Solve for the missing side of a right triangle if... A = 5 B = 12 C = ?
c = 13
Find the distance between points A and B if they have coordinates A(2, 3) and B(14, 12).
d = 15
Find the distance between the points (1, 5) and (3, 11) in simplest radical form.
d = 2√10
Find the distance between points (4, 1) and (-2, 10) in simplest radical form.
d = 3√13
What does dilating a point by a factor of 1/2 mean?
dividing x- and y-coordinates by 2
Figure out if triangle ABC with coordinates A(-3, 8), B(-9, 0), and C(5, 2) is isosceles.
it is isosceles! AB = 10 AC = 10
Use the distance formula to prove that P is the midpoint of MN. M (2, 3) P (10, 9) N (18, 15)
it is! MP = 10 PN = 10
Define median.
line extending from a vertex of a triangle to the *midpoint* of the opposite side
Define altitude.
line extending from a vertex of a triangle, *perpendicular* to the other side
Define concurrency.
point where 3 or more lines meet
The medians in a centroid are divided by the point of concurrency. What do we know about the length of the two divided parts?
the longer line segment is double the length of the smaller line segment, meaning the whole median is 3 times the length of the smaller line segment
The average of the x-values & the average of the y-values for 2 points is always...
the midpoint coordinates
What is an orthocenter?
the point of concurrency of the *altitudes* of a triangle
What is an incenter?
the point of concurrency of the *angle bisectors* of a triangle — creates congruent triangles
What is an centroid?
the point of concurrency of the *medians* of a triangle
What is a circumcenter?
the point of concurrency of the *perpendicular bisectors* of a triangle
What is the relationship between the line segments extending from the vertices to the circumcenter of the triangle?
they are equal
Determine the equation of the perpendicular bisector JK whose endpoints are J(-4, 9) and K(6, 1).
y = 5/4x + 15/4
A circle has a center located at (-2, 4) and a radius length of 10. Does the point (4, -4) lie on this circle?
yes
Find the midpoint of these points: (-8, 12) and (5, 4)
(- 3/2, 8)
Find the midpoint of these points: (-5, 7) and (9, 15)
(2, 11)
When can you use the Pythagorean Theorem?
- there is a right triangle - 2 side lengths are known
Point A is translated on a coordinate plane 3 units to the left and 9 units upward to produce A'. What best represents the length of segment AA'?
3√10
Which of the following would be true about the perpendicular bisector of the line segment whose endpoints are E(-3, 2) and F(9, 10)? 1) It would have a slope of 2/3 and pass through (3, 6) 2) It would have a slope of 2/3 and pass through (6, 12) 3) It would have a slope of -3/2 and pass through (6, 12) 4) It would have a slope of -3/2 and pass through (3, 6)
4
What best represents the distance between the y-intercept and x-intercept of a line whose equation is *y = 3x + 12*?
4√10
If two legs of an isosceles right triangle measure 7 inches, what represents the length of its hypotenuse?
7√2