Question

If you are given the measurements of two sides of a triangle, what would be true about the triangles you make?

Answer 1

ing Objective(s)·Identify equilateral, isosceles, scalene, acute, right, and obtuse triangles.·Identify whether triangles are similar, congruent,or neither.·Identify corresponding sides of congruent and similar triangles.·Find the missing measurements in a pair of similar triangles.·Solve application problems involving similar triangles.IntroductionGeometric shapes, also called figures, are an important part of the study of geometry. Thetriangleis one of the basic shapes in geometry. Itis the simplest shape within a classification of shapes calledpolygons. All triangles have three sides and three angles, but they come in many different shapes and sizes. Within the group of all triangles, the characteristics of a triangle’s sides and angles are used to classify it even further. Triangles have some important characteristics, and understanding these characteristics allows you to apply the ideas in real-world problems.Classifying and Naming TrianglesA polygon is a closed plane figure with three or more straight sides. Polygons each have a special name based on the number of sides they have. For example, the polygon with three sides is called a triangle because “tri” is a prefix that means “three.” Its name also indicates that this polygon has three angles. The prefix “poly” means many.The table below shows and describes three classifications of triangles. Notice how the types of angles in the triangle are used to classify the triangle.Name of TrianglePicture of TriangleDescriptionAcute TriangleA triangle with 3 acute angles (3 angles measuring between0° and 90°).Obtuse TriangleA triangle with 1 obtuse angle (1 angle measuring between 90° and 180°).Right TriangleA triangle containing one right angle (1 angle that measures90°). Note that the right angle is shown with a corner mark and does not need to be labeled 90°.The sum of the measures of the three interior angles of a triangle is always 180°. This fact can be applied to find the measure of the third angle of a triangle, if you are given the other two. Consider the examples below.ExampleProblemA triangle has two angles that measure 35° and 75°. Find the measure of the third angle.35° + 75° +x= 180°The sum of the three interior angles of a triangle is 180°.110º +x= 180ºFind the value ofx.x= 180° ‒ 110ºx= 70°AnswerThe third angle of the triangle measures 70°.ExampleProblemOne of the angles in a right triangle measures 57º.Find the measurement of the third angle.57° + 90° +x= 180°The sum of the three angles of a triangle is 180°.One of the angles has a measure of90° as it is a right triangle.147º +x= 180°Simplify.x= 180º - 147ºx= 33 ºFind the value ofx.AnswerThe third angle of the right triangle measures 33°.

Answer 2

It would be sure about the three sides of the triangle that the the summation of any two sides must be always greater than the third side.

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