Similar Triangle Proofs | MathHelp.com - By MathHelp.com
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| 00:0-1 | in this example , we're asked to determine if each | |
| 00:03 | of the following pairs of triangles are similar In part | |
| 00:07 | a notice that were only given one pair of congruent | |
| 00:11 | angles the 60° angles . But remember that the sum | |
| 00:20 | of the measures of the angles of a triangle is | |
| 00:22 | 180°. . So we can determine that the measure of | |
| 00:27 | the missing angle of the first triangle is 55° Because | |
| 00:35 | 65 plus 60 plus 55 equals 180 . Now we | |
| 00:42 | have two pairs of congruent angles , the 55° angles | |
| 00:51 | And the 60° Angles . Therefore , since two of | |
| 00:56 | the angles of one triangle are congruent to two of | |
| 00:59 | the angles of the other triangle , we can say | |
| 01:02 | that yes , the triangles are similar by the angle | |
| 01:06 | angle similarity postulate it . Yeah . Yeah . In | |
| 01:17 | part B since we're given that the lines at the | |
| 01:20 | top and the bottom of the figure are parallel , | |
| 01:23 | we can mark the alternate interior angles at the upper | |
| 01:27 | left and lower right as congruent because if two parallel | |
| 01:34 | lines are cut by a transfer cell , then alternate | |
| 01:38 | interior angles are congruent notice , however , that there | |
| 01:44 | are no other pairs of angles that can be marked | |
| 01:46 | as congruent . So we do not know if these | |
| 01:49 | triangles are similar because we only have one pair of | |
| 01:53 | congruent angles , so we cannot use the angle angle | |
| 01:57 | similarity postulate . In this situation , we write that | |
| 02:02 | the triangle similarity cannot be determined . Yeah . Yeah | |
| 02:19 | . In part C notice that the small triangle and | |
| 02:24 | the large triangle both have a right angle . Also | |
| 02:29 | noticed that these triangles share the angle at the lower | |
| 02:33 | left of the figure , so we can mark this | |
| 02:35 | angle as congruent to itself . Therefore , since two | |
| 02:41 | of the angles of the smaller triangle are congruent to | |
| 02:45 | two of the angles of the larger triangle . We | |
| 02:49 | can say that yes , these triangles are similar by | |
| 02:53 | the angle angle similarity postulate . |
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