U5 L5 Similar Triangles Skill Builder
Completion requirements
Unit 5
Applications of Derivatives
B. Related Rates Problems
Lesson 5: Related Motion
Skill Builder
Similar Triangles
Similar triangles are triangles that have the same shape, with the same three angle measures.Interactive
Click the interactive button to open the applet Similar Triangles. This applet explores a relationship that is true for all similar triangles.
Take a look at the diagram below showing three similar triangles. All three of the red sides correspond and all three of the blue sides correspond. Dividing the blue length of one triangle by the red length of the same triangle will give the same value for any of the three triangles.
Find the measure of side «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math».
Set up a proportion.
The measure of side «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» units.
Case 1:
Keep the information for each triangle in its own ratio. Make sure that the order of the sides are the same for both ratios. In this case «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»red«/mi»«mn»1«/mn»«/msub»«msub»«mi»blue«/mi»«mn»1«/mn»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»red«/mi»«mn»2«/mn»«/msub»«msub»«mi»blue«/mi»«mn»2«/mn»«/msub»«/mfrac»«/math».
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mn»6«/mn»«mn»9«/mn»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»x«/mi»«mn»3«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mn»9«/mn»«mi»x«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»18«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/math»
Case 2:
Keep the corresponding side of each triangle in a ratio. In this case, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»red«/mi»«mn»1«/mn»«/msub»«msub»«mi»red«/mi»«mn»2«/mn»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»blue«/mi»«mn»1«/mn»«/msub»«msub»«mi»blue«/mi»«mn»2«/mn»«/msub»«/mfrac»«/math».
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mn»6«/mn»«mi»x«/mi»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mn»9«/mn»«mn»3«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mn»9«/mn»«mi»x«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»18«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/math»
The measure of side «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math» units.