For congruent triangles JKL and TRS, state three pairs of congruent sides and three pairs of congruent angles. For example: Segment JL is congruent to Segment TS; Angle L is congruent to Angle S.

For congruent triangles DEF and PMN, state the pairs of congruent sides and the pairs of congruent angles.

Answer the following questions about the geometric design in the order given. State the letter of the question and then the answer. (a) How many small congruent equilateral triangles are in this design? (They may be black or white.) (b) How many larger congruent equilateral triangles are in this design? (They are made up of four smaller equilateral triangles.) (c) How many congruent parallelograms are in the design? (They are made of two smaller equilateral triangles.) (d) How many congruent trapezoids are in the design? (They are made up of three smaller equilateral triangles.) (e) How many smaller equilateral triangles make up the regular hexagon that is in the design?

Write four pairs of corresponding angles by naming their vertices.

Write four pairs of corresponding sides by naming their segments.

How many triangles in the triangle on the right are similar to the solid black triangle on the left? The white lines are the bottoms of different triangles.

State the name of the angle and measure for angles A, Y, and Z.

For similar triangles ABC and XYZ, state the value for “a” and the value for “y”? State the letter and then its value.

For the given right triangle, if one leg measures 18 and the hypotenuse measures 25, what is the length of the other leg? Use a calculator to find the square root and round answer to nearest tenth.

Pythagorean triples are three numbers where the sum of the squares of the two smaller numbers is equal to the sum of the square of the larger number. Find and state three sets of Pythagorean triples.

For example, 6, 8, 10 are Pythagorean triples because:

                          6² + 8² =  10²

                         36 + 64 =  100

                             100   =  100

The backboard on a basketball hoop is a square with an area of 10 square feet. Select the best estimate for the length of one side of the backboard.

What is the approximate length of the hypotenuse of the given right triangle with legs measuring 6 inches each? Round answer to nearest tenth.

The “scale factor” for similar triangles is the ratio that exists between the corresponding sides. Print out the picture and then answer the questions about the two similar triangles. State the letter and then the answer.

Printable Triangles

a.   Sides YZ and FG are corresponding sides.  These corresponding sides can be expressed as a ratio in fraction form,YZ/FG. Identify the other two pairs of corresponding sides and write them in fraction form.

b.  The length of “leg” YZ is 6 units, determined by counting the spaces between the dots along the side of triangle XYZ.  Write the name of the other “leg” in this triangle and then write its length.  Write the names of the “legs” of triangle EFG and then write the length for each leg.

c.   Identify the hypotenuses for each of the triangles and then calculate their lengths by using the Pythagorean Theorem. Write the name and length for both of the hypotenuses.

d.  Now using the actual lengths of the sides, write a fraction for the three pairs of corresponding sides.  Refer back to question “a” for the fractions for corresponding sides, and questions “b” and “c” for the actual lengths.

e.   Simplify each of the fractions written in “d”.  What is the scale factor for the two similar triangles?

Find the product. 8(–8)

Find the quotient. 

Which is larger?

What type of symmetry does the design show? Please explain.

The temperature at 7:00 am was –3º Fahrenheit.  By noon, it had increased by 10 Fahrenheit degrees.  What was the temperature at noon?  Explain how you found the temperature.

Note:  For the degree symbol, just write out the word “degrees”.

The given drawing is an example of two angles that share a common ray and are "complementary". The larger angle formed by combining the two smaller angles is a right angle. "Supplementary" angles are angles that total 180 degrees. On paper draw two angles that when pushed together to share a common ray form supplementary angles. Describe your drawing and state the size of each angle.

Look at the given right triangle which is not drawn to scale. Investigate what might be wrong with the given information. Briefly write your findings and justify your ideas by geometric principles.