Look at the statements below:

If a triangle has a right angle, then it is a right triangle.

If a triangle is a right triangle, then it has two acute angles.

In PQR, mQ = 90°.

Which of these statements must be true?

In the figure below, ΔABD and ΔCDB are isosceles triangles. The vertex angles, ABD and CDB and, are congruent as shown below.

• Prove that quadrilateral ABCD is a parallelogram.
   

If the pattern continues, which of these would be next in the pattern?

Isosceles triangle ABC is shown below. BD is the angle bisector of ABC.

• Prove that BD bisects AC.
   

One line divides a plane into two parts. Two distinct parallel lines divide a plane into three parts. Into how many parts will n distinct parallel lines divide the plane?

Consider these statements:

• Every square is a rhombus.
• Quadrilateral ABCD is not a rhombus.

Which of these conclusions can be made using both statements?

Look at the statements shown below:

• If the pencil is red, then the pen is white.
   
• If the protractor is not blue, then the compass is green.
   
• If the protractor is blue, then the pen is not white.
   

If the pencil is red, which of these conclusions can be drawn from the statements given?

ΔPQR is shown below. mQ > mR.

Which of these statements is true?

A pentagon has five diagonals, as shown below.

The chart below shows the relationship between the number of sides of a polygon and the number of diagonals in a polygon.

Based on this pattern, how many diagonals can be drawn in a 10-sided polygon?

Melanie, Nikki, and Donny are three students in a geometry class. Melanie is younger than Nikki, and Donny is older than Nikki.

Which of these must be true?

Study the pattern below.

What will be the next figure in the pattern?

• Prove is similar to .
• Railings cost $4 per foot. How much will it cost to put railings on both sides of the bridge? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Look at the statement below.

If two angles are vertical angles, then they are congruent.

Which of these statements can be concluded from the statement above?

• Prove that the ironing board is parallel to the floor.
   
• Use mathematics to justify that ABCD is a rectangle.
   

Look at the pattern below.

If the pattern continues, how many blocks will be in the next figure?

The statements below are true.

All simkos are temas.

All bollies are simkos.

Using deductive reasoning, which of these statements must also be true?

Study the pattern below.

If the pattern continues, what will be the next shape?

Look at the statements below.

1. If Jason is not here, then he is not well.
2. Jason is well.

Assuming that these two statements are true, what conclusion can be made?

Rectangle ABCD is shown below.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

A certain triangle has exactly two congruent angles. Which of these conclusions must be true?

Look at the pattern below.

If the pattern continues, how many triangles will be in the next figure?

Given:

is supplementary to .

is supplementary to .

Which of these statements must be true?