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Home > INT2 > Chapter 2 > Lesson 2.3.4 > Problem 2-114

2-114.

 Which pairs of triangles below are congruent and/or similar? For each part, explain how you know using an appropriate triangle congruence or similarity condition. Note: The diagrams are not necessarily drawn to scale.

What does it mean for two triangles to be congruent? What does it mean for two triangles to be similar?
How are these two definitions different?

  1. Two triangles. First triangle has side lengths 6 feet, 12 feet, and 15 feet. Second triangle has side lengths 2 feet, 4 feet, and 5 feet.

    Divide each side of the triangle on the left by .
    What do you notice?

  1. Two obtuse triangles. First triangle has a side length of 6 centimeters and an 20 degrees angle opposite that side. The obtuse angle is 112 degrees.  Second triangle has a side length of 6 centimeters and a 20 degree angle opposite that side.  The other acute angle is 48 degrees.

    congruent ( or )

  1. Two right triangles. First has a height of 12 meters and hypotenuse of 13 meters. Second has a base of 12 centimeters and height of 5 centimeters.

    Use the Pythagorean Theorem to solve for the missing side.

  1. Two triangles. First triangle has two angles, 48 and 62 degrees with a side length of 12 inches between the angles. Second triangle has 48 and 62 degree angles with a side length of 12 feet opposite the 48 degree angle.

    Where is the located on each triangle?

    similar () but not congruent since the two sides of length are not corresponding