Jana's Geometry Book
Table of Contents
- Introducing Geometry
- What is a circle?
- Reasoning in Geometry
- Alternate angles on parallel lines
- Angles on a Straight Line phone-friendly
- Mystic Rose and Handshakes
- Constructions
- Perpendicular Bisector Definition
- Triangle Properties
- Is "SSA" Legit? What Do You Think?
- AA Similarity
What is a circle?
Circle is the moving path of a point .[br]Circle is locus of points equidistant from a point.
What is a circle?
Alternate angles on parallel lines
Alternate angles on parallel lines
Perpendicular Bisector Definition
[color=#000000]In the applet below, [/color][b][color=#cc0000]line p[/color][/b][color=#000000] is said to be the [/color][b][color=#cc0000]perpendicular bisector[/color][/b][color=#000000] of the segment with [/color][i][b]A[/b][/i][color=#000000] and [/color][i][b]B[/b][/i][color=#000000] as [/color][b]endpoints[/b][color=#000000]. [br][br]Interact with this applet for a few minutes, then answer the questions that follow. [br][/color][i]Be sure to change the locations of points [b]A[/b] and [b]B[/b] each time before you re-slide the slider. [/i]
[color=#000000]Reset the applet and re-slide the slider just one more time. [br][br][b]Questions: [/b] [br][br]1) What can you conclude about the white point you see in the applet above? [br] How do you know this? [br][br]2) What is the measure of the [/color][b]gray angle[/b][color=#000000]? How do you know this to be true? [br][br]3) Given your responses for (1) and (2) above, write your own definition for the term[br] [/color][i][color=#cc0000]perpendicular bisector[/color][color=#000000]of a segment[/color][/i][color=#000000]. In essence, complete the following sentence definition: [br][br] A [/color][b][color=#cc0000]perpendicular bisector[/color][/b][color=#000000] [b]of a segment[/b] is...[/color]
Is "SSA" Legit? What Do You Think?
[color=#274e13][i]So far, we've learned a few theorems that help us prove two triangles congruent. Recall these theorems are:[/i][/color][br][br][b][color=#0000ff]The SSS Theorem[br]The SAS Theorem[br]The ASA Theorem[/color][/b][br][br]Yet, what about [color=#ff0000][b]"SSA"[/b][/color]? That is, [b][color=#ff0000]if we have 2 sides and a "non-included" angle of one triangle congruent to 2 sides and a "non-included" angle of another triangle, can we conclude that the two triangles are congruent[/color][/b]? [br][br]Interact with the applet below for a minute or two. (Feel free to move any of the big black points around.) Then answer the [color=#ff0000][b]question[/b][/color] above (in detail.)