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GeoGebra Slider AA Similar Triangles
Resource:
GeoGebra Slider AA Similar Triangles

Geometry & Algebra II Archive

Geo U3: Similarity and Proof

Big Idea: Big Idea 1

Slider that shows 2 similar triangles formed by parallel lines and 2 transversals.  The focus is on the vertical angles and the alternate interior angle pairs.

Open Resource
Type
Geometry: Similarity and Proof
File
External Link
Tags
angle, vertical, alternate interior, similar, triangle
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GeoGebra Slider that represents complementary and supplementary angle pairs
Resource:
GeoGebra Slider that represents complementary and supplementary angle pairs

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 1

Slider allows for the segment/ray length to change in order to see the relationship/lack of relationship between angle measures and ray lengths.

Open Resource
Type
Geometry: Proofs About Congruence
File
External Link
Tags
angle, supplementary, complementary
Standards
Common Core: Major Standards ( G-CO.C.9 ) Common Core: Supporting Standards ( G…
+— Details
Common Core: Major Standards:
G-CO.C.9

Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

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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GeoGebra Slider that shows the sum of the interior angles of a triangle equal 180 degrees
Resource:
GeoGebra Slider that shows the sum of the interior angles of a triangle equal 180 degrees

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 2

Slider shows that all 3 angles in a triangle add to 180 degrees.  Can be used to classify triangles as acute, obtuse, right, scalene, isosceles, equilateral.  Can be used to analyze angle side relationships.

Open Resource
Type
Geometry: Proofs About Congruence
File
External Link
Tags
triangle, angle
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GeoGebra Visual of Reflex and "Non-Reflex" Angles
Resource:
GeoGebra Visual of Reflex and "Non-Reflex" Angles

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 1

Sliders that demonstrate angle measures (Reflex and "Non-Reflex" angles) independent of ray length.

Open Resource
Type
Geometry: Proofs About Congruence
File
External Link
Tags
angle
Standards
Common Core: Major Standards ( G-CO.C.9 ) Common Core: Supporting Standards ( G…
+— Details
Common Core: Major Standards:
G-CO.C.9

Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

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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Inscribing a Triangle in a Circle
Resource:
Inscribing a Triangle in a Circle

Geometry & Algebra II Archive

Geo U6: Circles

Big Idea: Big Idea 3

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter. 

Open Resource
Type
Geometry: Circles
File
External Link
Tags
inscribe, circle, angle
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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.

Open Resource
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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Slider that demonstrates Angle-Side-Side triangles
Resource:
Slider that demonstrates Angle-Side-Side triangles

Geometry & Algebra II Archive

Geo U2: Proofs about Congruence

Big Idea: Big Idea 3

Slider that can visually show the different possible triangles that exist if trying to use Angle-Side-Side.

Open Resource
Type
Geometry: Proofs About Congruence
File
External Link
Tags
angle, side
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