Mathematics exam 2

Mathematics exam 2

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angles are if the sum of their is equal to 90 angles are if the sum of their is equal to 180 angles have the same vertex, share a side, and do not sum of the measures of all adjacent angles same vertex is equal to 360 of two lines two sets of vertical angles are formed. Vertical angles measures and are to m∠1 = m∠3 and m∠2 = m∠4 ■ m∠1 + m∠2 = 180 and m∠2 + m∠3 = 180 ■ m∠3 + m∠4 = 180 and m∠1 + m∠4 = Angles and angles and lines are said to be bisected into two parts with equal segment AB is bisected at point to the figure, ∠A is bisected by ray C + ∠2 + ∠3 + ∠4 = and ∠2 are + ∠2 = + ∠2 = AND Formed by Parallel two parallel lines are by a third angles are Of these vertical angles, four will be equal four will be equal and obtuse, or all four will be right Any of an acute and an obtuse be the above ∠b, ∠c, ∠f, and ∠g are all acute and equal. ■ ∠a, ∠d, ∠e, and ∠h are all obtuse and equal. ■ Also, any acute angle added to any obtuse be + m∠d = 180° m∠c + m∠e = 180° m∠f + m∠h = 180° m∠g + m∠a = the figure below, if m || n and a || b, what is the value of both sets of lines are parallel, you know that x can be added to x + 10 to equal 180. is thus, x + x + 10 = for x: 2x + 10 = 180 −10 = = m∠x = 85° and the obtuse angle is equal to 180 − 85 = of a measures of the three angles in a triangle 180 exterior angle can be formed by extending a side from any of the three vertices of a triangle. Here are some rules for working with exterior An exterior angle and interior angle that share the same vertex are d d + c = 180° and d = b + + b + c = 180° x ° (x + b e f c AND An exterior angle is equal to the sum of the interior The sum of the exterior angles of a 360 Tr is possible to classify triangles into three on the number of equal Isosceles (no equal sides) (two equal sides) (all sides is also possible to classify triangles into three based on the measure of the greatest Right Obtuse angle greatest angle greatest angle is acute is 90° is the in and right triangles will be useful in taking the GED exam. ■ In isosceles equal angles are sides. ■ In all sides are equal and are a C m∠a = AND In a right triangle, the side opposite the is called the This will be side of the right theorem is an important tool for work- ing with right It states: a2 + b2 = c2, where a and b represent the legs and c the theorem allows you to find the length of any side as along as you know the measure of the other two. a2 + b2 = c 2 12 + 22 = c 2 1 + 4 = c 2 5 = c 2 �5� = Right right triangle with two angles each measuring is called an isosceles right triangle. In an The length of the is �2� by the length of one of the legs of the The length of each leg is ��2 2�� by of the = y = × �11 0 � = 10 = a right triangle with the other angles measuring 30 and 60 The leg opposite the 30-degree angle is half of the (And, is two times the length of the the 30-degree The leg opposite the 60-degree angle is �3� times the length of the other AND = 2 × 7 = 14 and y = are said to be congruent by the sym- bol �) when they have exactly the same size and triangles are congruent if their angles and sides) are it is easy to tell if two triangles are congruent by in geometry, you must be able to prove that are two triangles are one of the three listed below must be (SSS) The side measures for are the (SAS) The sides and the them are the (ASA) Two angles and the them are the Are triangles �ABC and ∠ABD is congruent to ∠CBD and ∠ADB is congruent to ∠CDB. Both triangles share side BD. Step 1: Mark the given on 2: Determine whether this is to prove the triangles two angles and the side between them Using the ASA rule, you can triangle ABD is congruent to triangle CBD. � Polygons and Paral le polygon is a closed figure with three or more Related to Vertices are corner points, also called a polygon. The vertices in the above A, B, C, D, E, and F. ■ A diagonal of a polygon is a line segment vertices. The two diagonals in the polygon above are line segments BF and AE. ■ A regular polygon has sides and angles that are An polygon has angles that are of a is a polygon. Since a can be divided by a diagonal into two AND sum of its interior angles will equal 180 + 180 = + m∠b + m∠c + m∠d = Angles To find the sum of the interior angles of any polygon, use this = 180(x − 2)°, with x being the number the sum of the angles in this = (5 − 2) × 180° S = 3 × 180° S = to the exterior angles of a triangle, the sum of angles of any polygon equals 360 two polygons are similar, their equal and the ratios of the sides are two polygons are similar because are equal and the ratios of the sides are in is a with two pairs of the figure above, line AB || CD and BC || AD. A has: ■ opposite sides that are equal (AB = CD and BC = AD) ■ opposite angles that are equal (m∠a = m∠c and m∠b = m∠d) ■ angles that are (m∠a + m∠b = 180°, m∠b + m∠c = 180°, m∠c + m∠d = 180°, m∠d + m∠a = TYPES OF A rectangle is a that has four C AB = CD DA B AND