Theorems on Square: Activity 10 - Especially For You
Do the procedures below and answer the questions that follow.
1. Draw square GOLD.[br]2. Draw diagonals GL and OD that meet at C.[br]3. Measure all the segments.[br]4. Measure all the angles.
[table][tr][td]What to measure[/td][td][math]\angle GDL[/math][/td][td]GL and OD[/td][td][math]\angle GCO[/math] and [math]\angle OCL[/math][/td][td][math]\angle GDO[/math] and [math]\angle ODL[/math][/td][td][math]\angle GOD[/math] and [math]\angle LOD[/math][/td][/tr][tr][td]Measurement[/td][td][/td][td][/td][td][/td][td][/td][td][/td][/tr][/table]
[table][tr][td]What to measure[/td][td][math]\angle GDL[/math][/td][td]GL and OD[/td][td][math]\angle GCO[/math] and [math]\angle OCL[/math][/td][td][math]\angle GDO[/math] and [math]\angle ODL[/math][/td][td][math]\angle GOD[/math] and [math]\angle LOD[/math][/td][/tr][tr][td]Measurement[/td][td][/td][td][/td][td][/td][td][/td][td][/td][/tr][/table]
What is the measure of [math]\angle[/math]GDL?
If [math]\angle[/math]GDL is a right angle, can you consider square a rectangle? If yes, what theorem on rectangle justifies that a square is a rectangle?
What can you say about the lengths of GL and DO?
If GL and DO have the same measures, can you consider square a rectangle? If yes, what theorem on rectangles justifies that a square is a rectangle?[br]
What can you say about the measures of [math]\angle GCO[/math] and [math]\angle OCL[/math]?
If GL and DO meet to form right angles, can you consider a square a rhombus? If yes, what theorem on rhombus justifies that a square is a rhombus?
What can you say about the measures of [math]\angle GDO[/math] and [math]\angle ODL[/math] as a pair and [math]\angle GOD[/math] and [math]\angle LOD[/math] as another pair?
If GL divides opposite angles equally, can you consider a square a rhombus? If yes, what theorem on rhombus justifies that a square is a rhombus?