Visualization, Reasoning and Proof, and SimilarityYou can show that two triangles are similar when certain relationships exist betweentwo or three pairs of corresponding parts. If you know two triangles are similar, thenyou know their corresponding sides are proportional.Task 1In the diagram below, AC 6 DF 6 BH and CB 6 FE.A DC GBHFEa. Find four similar triangles. Explain how you know that they are all similar.b. Using the similar triangles you found in part (a), complete the followingextended proportion:ABAC 5 DEj 5 jDG 5 jj

Frances drew ΔΔABC and ΔΔDEF so that A D, AB = 4, DE = 8, AC = 6, and DF = 12. AreΔΔABC and ΔΔDEF similar? If so, identify the similarity postulate or theorem that applies.A.Similar - AAB.Similar - SASC.Cannot be determinedD.Similar - SSS

Match the definition with the correct word.Two pairs of proportional sides and a pair of equal included angles determine similar triangles.Answer 1 Question 18If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.Answer 2 Question 18If all three pairs of sides of corresponding triangles are in proportion, the triangles are similarAnswer 3 Question 18

Determine if triangle F, G, HFGH and triangle I, J, KIJK are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)FGHIJK271549°1357549°100AnswerAttempt 2 out of 2The triangles similar .

From the diagram below, we can tell that ____.Question 4Select one:a.the two triangles are congruentb.the two triangles are not similarc.the two triangles are similar by SASd.the two triangles are similar by SSS

For each statement, write A if the statement is always true, S if the statement is sometimes true, and N if the statement is never true.1. Two rectangles are similar.2. Two rhombi are similar.4.3. Two squares are similar.4. Two equilateral triangles are similar.5. Two isosceles trapezoids are similar.6. A quadrilateral is similar to a pentagon.7. A right triangle is similar to an equilateral triangle.8. If AABC = ADEF and ADEF ~AXYZ, then AABC~AXYZ.9. Two congruent triangles are similar.10. Two similar triangles are congruent