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Classifying Triangles based on angle measures
Resource:
Classifying Triangles based on angle measures

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 2

Students solve for missing interior angles in triangles.  Triangles are on individual cards.  Students determine appropriate "angle" and "side" terms (acute, obtuse, right, scalene, isosceles, equilateral) and place the triangle cards into the table.  Opportunity to address why certain descriptions are impossible (such as an equilateral right triangle) and why it's impossible to have a triangle with more than 1 obtuse angle.

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Type
Geometry: Proofs About Congruence
File
Google Doc
Tags
acute, obtuse, right, scalene, isosceles, equilateral, triangle
Standards
Common Core: Major Standards ( G-CO.C.10 ) Common Core: Supporting Standards ( …
+— Details
Common Core: Major Standards:
G-CO.C.10

Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Clarification: Theorems include but are not limited to the listed theorems. Example: an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle

Common Core: Supporting Standards:
G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

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Finding the Height of Your School
Resource:
Finding the Height of Your School

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

Using right triangle trigonometry, students will be able to find the height of the school building.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
right, triangle, trigonometry
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
G-SRT.C.6

Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.C.7

Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT.C.8

Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

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Parallax
Resource:
Parallax

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

Students will use distant buildings and the changing angles as they move in 1 direction to apply trig and find missing distances.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
trigonometry, right, triangles
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
G-SRT.C.6

Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.C.7

Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT.C.8

Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

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Right Triangles Inscribed in Circles 1
Resource:
Right Triangles Inscribed in Circles 1

Geometry & Algebra II Archive

Geo U6: Circles

Big Idea: Big Idea 3

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

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Type
Geometry: Circles
File
External Link
Tags
circle, right, triangle, inscribed, angle
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Right Triangles Inscribed in Circles 2
Resource:
Right Triangles Inscribed in Circles 2

Geometry & Algebra II Archive

Geo U6: Circles

Big Idea: Big Idea 3

The result here complements the fact, presented in the task ''Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle. 

Open Resource
Type
Geometry: Circles
File
External Link
Tags
circle, right, triangle, inscribed, angle
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