Day #1 Review

In 

∆SRK below, medians SC, KE, and RL intersect at M. Which statement must always be true?

• 3MC=SC

• MC=1/3(SM)

• RM=2MC

• SM=KM

Answer explanation

The three medians of a triangle meet at a centroid, which is point M. The distance from the angle to the centroid is ALWAYS twice as much as from the centroid to the midpoint of the opposite side.

In the diagram below, AB || DEF, AE and BD intersect at C, m ∠B = 43°, and m ∠CEF = 152°. Which statement is true?

• m<D = 28°

• m<A = 43°

• m<ACD = 71°

• m<BCE = 109°

Answer explanation

Because of alternate interior angles, angle D = 43 degrees. Angle CED is supplementary to 152 degrees, so it must be 180 - 152 = 28 degrees. By the Exterior Angle Theorem, Angle ACD must be the sum of the two remote angles, D and CED.

Which of the following is the construction of a median?

• 
• 
• 
• 

Answer explanation

Construct a Median - YouTube

What is an equation of the line that passes through the point 

(6,8) and is perpendicular to a line with equation y= (3/2) x+5?

• y-8= (3/2) x-6  

• y-8= (-2/3) x-6

• y+8= (3/2) x+6

• y+8= (-2/3) x+6

Answer explanation

Perpendicular means that the slope of the new line is -2/3, so eliminate choices (1) and (3), which are parallel. Point-slope form is y - y₀ = m(x - x₀). Note the signs. Plug in 6 for x₀ and 8 for y₀

Triangle ABC has vertices with coordinates

A(– 1, 1) B (4,0), and C (0,4). Prove that 

∆ABC is an isosceles triangle but not an equilateral triangle. 

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OFF

Answer explanation

First you would need to prove the legs are perpendicular to prove that it is a right triangle. Then you would need to prove that its legs are congruent to show that it is an isosceles triangle. To prove it is not equilateral, you would have to prove that the hypotenuse is not congruent.

Directed line segment DE has endpoints 

D(-4,-2) and E(1,8). Point F divides DE such that DF:FE is 2:3. What are the coordinates of F?

• (-3,0)

• (-2,2)

• (-1,4)

• (2,4)

Answer explanation

2 + 3 = 5, so point F is 2/5 of the way from D to E.1 - (-4) = 5, and (2/5)(5) = 2. Add 2 to -4 and you get -2, which must be the x-coordinate for F .8 - (-2) = 10, and (2/5)(10) = 4. Add 4 to -2 and you get 2, which must be the y-coordinate for F.

Which equation represents a line parallel to the line whose equation is

−2x + 3y = −4 and passes through the point (1,3)

• y − 3 = −3/2 (x − 1)

• y − 3 = 2/3 (x − 1)

• y + 3 = −3/2 (x + 1)

• y + 3 = 2/3 (x + 1)

Answer explanation

You can solve for y to solve for the slope.

The vertices of quadrilateral MATH have coordinates M (−4,2), A (−1, −3), T (9,3), and H (6,8). Prove that quadrilateral MATH is a parallelogram. Prove that quadrilateral MATH is a rectangle.

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OFF

Answer explanation

First you would need to prove that opposite sides are parallel. Then you would need to prove that two consecutive sides form a right angle.

As shown in the diagram below, CD is a median of Triangle ABC. Which statement is always true?

• AD ≅ DB

• AC ≅ AD

• ∠ACD ≅ ∠CDB

• ∠BCD ≅ ∠ACD

Answer explanation

Medians split the line that they intersect.

As shown in the diagram below, ABC is parallel to EFG and BF ≅ EF.

If m ∠CBF = 42.5°, then m ∠EBF is

• 42.5°

• 68.75°

• 95°

• 137.5°

Answer explanation

Think about alternate interior angles and properties of different types of triangles.