Similar+Triangles+Part+II

**__Similar Triangles Part II__** Here is an online tutorial to view as a class. media type="youtube" key="s4fr9vC9C5Q?rel=0" height="360" width="480" align="center"

Open the file with the notes for today's lesson and then save the file to your laptop.

Work through these questions to discover more of the key properties of similar triangles. ﻿1. Triangle ABC has angles of 25, 30 and 125 degrees. Copies of triangle ABC have been used to make the grid which has three sets of parallel lines.  a) Are the matching sides of triangle ABC and triangle DEF in the same ratio?  b) Why does angle A = angle D, angle E = angle B and angle F = angle C?   2. Triangles XYZ and AZB have been drawn on a grid based on parallelograms.  a) What is the value of the ratios ZB:YZ, AB:XZ, AZ:XY? b) Why are all the small triangles congruent? c) Are the matching angles of triangle XYZ and AZB equal?  ﻿Two triangles are similar if the ratios of matching sides are equal.  This means that matching angles are equal.   <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 150%;">3. Identify the triangles that are similar in the following questions by looking for sides that are in the same ratio.  <span style="font-family: 'Comic Sans MS',cursive;">  <span style="font-family: 'Comic Sans MS',cursive;"> <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">﻿  <span style="background-color: #ffffff; color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">4. Each of the triangles A to J is similar to one of the triangles K to W. Match the triangles that are similar. <span style="font-family: 'Comic Sans MS',cursive;"> <span style="font-family: 'Comic Sans MS',cursive;"> <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 150%;">5. In triangle ABC and DEF, DE:AB = EF:BC = 2 and angle B = angle E <span style="font-family: 'Comic Sans MS',cursive;"> <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 150%;">What else would need to be known before we could say that the triangles are similar? <span style="background-color: #ffffff; color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">6. In the diagram, a grid based on parallelograms formed from triangle ABC is shown. Triangle DEF is shown on the grid. <span style="font-family: 'Comic Sans MS',cursive;"> <span style="background-color: #ffffff; color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">a) Why does angle A = angle D and angle C = angle F? <span style="background-color: #ffffff; color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">b) Does DF:AC = 2? <span style="background-color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 200%;">Two triangles are similar if an angle of one triangle is equal to an angle of the other and the lengths of the corresponding sides that form the angles are in the same ratio (this is like the SAS rule for congruent triangles). <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 150%;">7. Identify the pair of similar triangles in each of the following. <span style="font-family: 'Comic Sans MS',cursive;"> <span style="font-family: 'Comic Sans MS',cursive;"> <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Now try this activity from the Tale4Students site by entering the save code X040E on the right. <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Tale4Students <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Here is an extension question for fast finishers. <span style="background-color: #ffffff; color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">8. Find two similar triangles in each of the following. State which condition could be used to show that the triangles are similar. <span style="font-family: 'Comic Sans MS',cursive;">