Properties of Triangles and Proportions

The video tutorial reviews key concepts from chapter seven, focusing on solving word problems, understanding ratios, and using cross multiplication for proportions. It covers geometry topics such as perimeter, angles, similar triangles, midsegments, parallel lines, and angle bisectors, providing examples and explanations to prepare students for the test.

What is the ratio of boys to girls if there are 5 boys and 10 girls in a class?

• 10:5

• 5:10

• 2:1

• 1:2

How do you solve a proportion like 3/4 = x/8?

• Add 4 to both sides

• Cross-multiply and solve for x

• Divide both sides by 8

• Subtract 3 from both sides

If the perimeter of a triangle is 30 inches and the sides are in the ratio 2:3:4, what is the length of the longest side?

• 10 inches

• 12 inches

• 15 inches

• 20 inches

What do the angles of a triangle always add up to?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

In similar triangles ABC and DEF, if angle A corresponds to angle D, which side of triangle DEF corresponds to side AB?

• EF

• DF

• None of these

• DE

How do you determine which sides are in proportion in similar triangles?

• By their lengths

• By their colors

• By their angles

• By their positions opposite equal angles

What is a mid-segment of a triangle?

• A line connecting two vertices

• A line bisecting an angle

• A line parallel to one side and half its length

• A line perpendicular to one side

If a mid-segment of a triangle is 5 units long, what is the length of the side parallel to it?

• 20 units

• 15 units

• 10 units

• 5 units

What is the relationship between parallel lines and transversals?

• They form right angles

• They form congruent corresponding angles

• They form congruent alternate interior angles

• They form congruent exterior angles

In a triangle with equal segments, if one segment is 3x + 2 and the other is 11, what is the value of x?

• 6

• 5

• 4

• 3