![]() Sometimes, like the picture above, one will not receive a problem that requires AA~ or SAS~, and in those times, the SAS~ Theorem is and easy but efficient tool to use. Reasoning: This theorem is easy to interpret, and plays as a key theorem to prove whether two triangles are congruent. By the SAS~ Theorem, Triangle ABC ~ Triangle DEF because two sides of one triangle are proportional to two sides of another triangle and the included angle are congruent. BC and EF are corresponding sides, and the ratio they form is 8:4, which simplifies to 2:1 as well. AB and DE are corresponding, and the ratio they form is 6:3, which simplifies to 2:1. Because both are right triangles, that means both have one right angle. Triangle ABC has side lengths of 6 cm and 8 cm and Triangle DEF has side lengths of 3 cm and 4 cm. The picture above has two right triangles ABC and DEF. This postulate is also important because one of the ways to prove the Triangle Proportionality Theorem without doubt is by using the AA~ Postulate.Ä£) Side - Angle - Side Similarity Theorem: (Not to be confused with Side - Angle - Side Congruence Theorem) If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar. Another reason why the AA~ Postulate was put in this list was because it is one of the essential ways of finding if two triangles are similar, along with SAS~ and SSS~. For example, the only way to prove Theorem 1 (when not knowing the side lengths) listed above is to use AA~. Reasoning: Although this postulate is very simple to understand and use, the AA~ Postulate plays a key role in understanding lessons in this unit. Two polygons are similar if all corresponding angles are congruent and if the ratios of the measures of the corresponding sides are equal in this case Triangle ABC ~ Triangle EDF. This means all corresponding angles are congruent in the two triangles. If By the triangle sum theorem, When this theorem was introduced in Lesson 4, it seemed like it had very little application. Reasoning: Although this theorem has no name and we don't see this applied very often in our world, Theorem 1 is still essential to memorize to get through Geometry. Triangle ABC ~ Triangle DBA ~ Triangle DAC If Triangle ABC ~ Triangle DBA and Triangle ABC ~ Triangle DAC, then by the transitive property, Triangle DBA ~ Triangle DAC. Triangle ABC ~ Triangle DAC by AA~ because both have right angles and by the reflexive property,
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