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# Journal 4

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### Journal 4

1. 1. By: Esteban Lara<br />Journal 4<br />
2. 2. Types of Triangles<br />5 types of triangles would be acute triangles, obtuse triangles, right triangles, scalene triangle and the equilateral triangle also the isosceles triangle. We can classify triangles by the measurement of its angles and by side length.<br />
3. 3. Parts of a Triangle<br />A triangle is formed up by three angles and three sides and three vertexes (which are the corners). The interior angles are formed by two sides of the triangle and the exterior is formed by one side of the triangle and extension of an adjacent side. The sum theory angle says that the sum of the angles of a triangle is 180 degrees.<br />The interior angles are blue and the exterior angles are red and if you add the measurement of the blue angles, it would be 180. As you can see, there are three blue interior angle and three exterior angles.<br />
4. 4. Exterior Angles Theorem<br />The measure of an exterior angle of a triangle is equal to the sum of the measures of its opposite exterior angle. This means that the sum of two angles would be the measurement of the third one. It can be used to find the measurement of one of the angles in case you only have the measurement of two. But it can only be used when the ones you’re adding are opposite.<br />
5. 5. Examples:<br />Here you can see how the green numbers are added to find the gray. <60+<60=<120<br />(6x-1)+(5x+17)<br />11x+16=126<br />11x=110<br />x=10<br /><50+<90=<140<br />
6. 6. Congruence for Shapes and CPCT<br />Congruence for shapes means that a shape is the same size and shape as another. CPCT is corresponding parts of congruent triangles, which means that if two triangles are congruent, then all of their parts are also congruent.<br />Examples:<br />
7. 7. SSS<br />If the three sides of a triangle are congruent to the sides of another, then the triangles are also congruent.<br />Examples:<br />a<br />b<br />a<br />zet<br />tak<br />c<br />b<br />a≅-a, b≅-b, c≅-c<br />lmfao<br />c<br />a≅e, b≅d, c≅f<br />abc≅def<br />-b<br />-a<br />d<br />e<br />larlo<br />rol<br />-c<br />zet≅larlo, lmfao≅tron,<br />tak≅rol<br />f<br />tron<br />
8. 8. SAS<br />If two sides and the adjacent angle between them are congruent to the two sides and adjacent angle between them on another triangle, then the triangles are congruent.<br />Examples:<br />
9. 9. ASA<br />If two angles and the side between them are congruent to the two angles and the side between them on another triangle, then the two triangles are congruent.<br />Examples:<br />
10. 10. AAS<br />If two angles and a non-included side from a triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are congruent.<br />Examples:<br />3a<br />2a<br />1b<br />2b<br />1a<br />3b<br />