Exploring AIR Test Geometry Concepts

This video tutorial covers a range of mathematical concepts, starting with an introduction to problem 16 and a review of trigonometric functions like sine and cosine. It then delves into geometric proofs, focusing on congruence and the properties of isosceles triangles. The video also explains dilations and transformations in geometry, followed by a section on completing and interpreting frequency tables. The tutorial aims to reinforce understanding through step-by-step explanations and practical examples.

What is the sine of an angle in a right-angled triangle?

• Opposite over adjacent

• Adjacent over opposite

• Adjacent over hypotenuse

• Opposite over hypotenuse

What property states that congruent angles have equal measures?

• Addition property of equality

• Congruent angles property

• Base angles theorem

• Angle addition postulate

In an isosceles triangle, which angles are congruent?

• Vertex angles

• Adjacent angles

• Base angles

• Opposite angles

What does the angle addition postulate state?

• The measure of an angle is twice the sum of its complementary angles.

• Two adjacent angles add up to 180 degrees.

• The measure of an angle is equal to the sum of the measures of two angles that compose it.

• The sum of two angles equals the measure of their adjacent angle.

Which of the following is a property used to prove congruent triangles?

• SSS (Side-Side-Side)

• SAS (Side-Angle-Side)

• ASA (Angle-Side-Angle)

• All of the above

What remains unchanged in a dilation of a line?

• Y-intercept

• Slope

• Neither slope nor y-intercept

• Both slope and y-intercept

What transformation does not guarantee congruent figures?

• Reflection

• Translation

• Rotation

• Dilation

What is the y-intercept after a dilation with a scale factor of 6?

• -10

• 6

• -5/3

• 2

What is the result of a 60% of 70 in the context of the frequency table problem?

• 42

• 28

• 34

• 16

What is the correct calculation for the number of students who do not like popcorn but like candy?

• 58 - 42

• 70 - 42

• 50 - 42

• 50 - 16