Students will be able to apply the Pythagorean Theorem to find the height of an isosceles triangle, prove the distance formula, and classify a triangle as acute, right, or obtuse.
Students will be assessed through a worksheet that includes problems requiring them to apply the Pythagorean Theorem to find the height of an isosceles triangle, prove the distance formula, and classify triangles.
Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two other sides (a^2 + b^2 = c^2).
Height of an Isosceles Triangle: To find the height of an isosceles triangle, the Pythagorean Theorem can be used to relate the base and height of the triangle.
Distance Formula: The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points in a coordinate system.
Triangle Classification: Triangles can be classified as acute (all angles < 90 degrees), right (one angle = 90 degrees), or obtuse (one angle > 90 degrees) based on their side lengths.
Engage students by asking, "How can we use the Pythagorean Theorem in real-life situations?"
Show a short video or image of a triangle to spark curiosity
Discuss the Pythagorean Theorem and its formula
Explain how to find the height of an isosceles triangle using the Pythagorean Theorem
Anticipate common misconception: Students might confuse the legs and hypotenuse of a triangle
Provide examples for finding the height of an isosceles triangle step by step
Scaffold questions starting with basic calculations leading to more complex problems
Monitor student performance by circulating the classroom and offering guidance as needed
Assign problems requiring students to apply the Pythagorean Theorem to find the height of different isosceles triangles
Students will also prove the distance formula and classify triangles independently
Encourage students to show all their work and explanations clearly
Have students share their findings and explain how they used the Pythagorean Theorem
Summarize the key points covered during the lesson
Create a challenge for students to find the height of irregular triangles using the Pythagorean Theorem
Students are required to complete a set of problems similar to the ones covered in class, focusing on applying the Pythagorean Theorem to different triangle scenarios.
CCSS.MATH.CONTENT.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
CCSS.MATH.CONTENT.HSG.SRT.C.8b: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.