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Geometry 4-6 Complete Lesson: Congruence in Right Triangles

By Matt Richardson
Last updated about 3 years ago
27 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! One of the tent flaps was damaged in a storm. Can you use the other flap as a pattern to replace it?

Explain. You may also use the canvas to help illustrate your explanation.

Take Note: Explain why Side-Side-Angle is not a valid method for proving two triangles congruent. You may also use the can canvas to help illustrate your explanation.

Take Note: Define hypotenuse (of a right triangle). On the canvas, sketch a right triangle and label its hypotenuse.

Take Note: Define leg (of a right triangle). On the canvas, sketch a right triangle and label its legs.

Take Note: Sumamrize The Hypotenuse-Leg (HL) Theorem. You may use the canvas to help illustrate your description.

Problem 1 Got It? Complete the proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 1 Got It? Reasoning: Your friend says, "Suppose you have two triangles with congruent hypotenuses and one pair of congruent legs. It does not matter which leg in the first triangle is congruent to which leg in the second triangle. The triangles will be congruent." Is your friend correct? Explain. You may also use the canvas to help illustrate your explanation.

Problem 2 Got It? Complete the proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Vocabulary: A right triangle has side lengths of 5 cm, 12 cm, and 13 cm. What is the length of the hypotenuse?

Vocabulary: Explain how you identified the hypotenuse in the previous item.

Compare and Contrast: How do the HL Theorem and the SAS Postulate compare? How are they different? Explain.

Error Analysis: Your classmate says that there is not enough information to determine whether the two triangles shown are congruent. Is your classmate correct?

Explain. You may also use the canvas to help illustrate your explanation.

Review Lesson 4-5: Consider the congruence statement.

What type of triangle must â–³STU be?
Consider sketching â–³STU and labeling all known information.

Review Lesson 4-5: Consider the congruence statement.

What type of triangle must â–³STU be?
Consider sketching â–³STU and labeling all known information.

Review Lessons 4-3 & 4-6: Can you conlude that the triangles are congruent? Explain.

Vocabulary Review: True or False? Segments that are congruent have the same length.

Vocabulary Review: True or False? Polygons that are congruent have the same shape but are not always the same size.

Vocabulary Review: True or False? In congruent figures, corresponding angles have the same measure.

Use Your Vocabulary: Complete each sentence on the right with the appropriate items from the left.

  • is
  • is not
  • 1
  • 2
  • 3
  • equal to
  • greater than
  • less than
  • One side of a right triangle __?__ a hypotenuse.
  • A right triangle has __?__ legs.
  • The length of the hypotenuse is always __?__ the lengths of the legs.

Use Your Vocabulary: Refer to the diagram and categorize each side from the left column as either a hypotenuse or a leg of its respective triangle.

  • \overline{DF}
  • \overline{HI}
  • \overline{BA}
  • \overline{BC}
  • \overline{HG}
  • \overline{DE}
  • Hypotenuses
  • Legs

Reflection: Math Success