Download Geometry Level 8

Academy of Math
Geometry – Level 8 Guided Notes In this activity you will be working with lines, angles, triangles, motion geometry, and rotational symmetry 1. There are different kinds of lines: A Line ______________is a straight line with two endpoints A ________ is part of a line that goes in one direction starting from a single endpoint A _________ goes in both directions without endpoints 2. Line segments, Rays, and Lines can be___________, they go from side to side OR they can be__________, they go up and down An _________ Line is neither horizontal nor vertical 3. When line segments cross we say they intersect The point at which they intersect is called the point of intersection When intersecting lines form a square corner or right angle they are called _______________ Lines that travel in the same direction and never meet or change their distance from one another are called _______________ When lines are parallel they are marked with arrows 1 A __________ Line is a straight line segment that joins opposite corners on a polygon When lines are equal in length, they are marked with small dashes 4. __________ are formed when two lines share one endpoint Line segment AB and line segment BC share the endpoint B The shared endpoint is called the ___________ When naming an angle the vertex letter is always in the middle, this is angle ABC 5. Angles are measured and drawn by a ______________which uses units called __________ (o) When an angle forms a square corner it is called a _________ Angle; a right angle measures 90o An ________ Angle measure less than 90o An ____________ Angle measures greater than 90o but less than 180o A ____________ Angle measures 180o 2 6. ________________ Angles: angles formed by intersecting lines have a common vertex and the angles that are opposite to one another are always congruent Angle CFB and angle EFG are Opposite Angles and are the same size and shape Angle CFE and angle BFG are also opposite angles and the same size and shape 7. ___________ Angles have a common vertex and share one arm; adjacent angles are next to each other and are formed when an angle is bisected Angle ABC has been bisected to form angles ABD and DBC Adjacent angles are called __________________when the sum of the angles equals 90o The sum of angle QRS and angle SRT equals 90o, so these angles are complimentary Adjacent angles are called ________________when the sum of the two angles equals 180o The sum of angle DEF and FEG equals 180o, so these are supplementary angles When a third line, called a____________, intersects two parallel lines four angles are formed These angles are called _______________ Angles 3 The four pairs of corresponding angles are 1 & 5, 2 & 6, 3 & 7 and 4 & 8 8. Angles are sometimes used to name types of triangles *Remember that a triangle is a three‐sided polygon A _________‐Angled Triangle has one 90o angle An _____________‐Triangle has three equal sides An _________‐Angled Triangle has one angle greater than 90o but less than 180o An _______‐Angled Triangle has all three angles measuring less than 90o Whatever the shape of the triangle, the sum of the angles always equals 180o 9. Triangles can also be named based on the nature of the triangle sides An ____________‐Triangle has two equal sides 4 A __________‐Triangle has three unequal sides 10. If the figures are the same shape but different sizes the figures are ___________but not congruent There are two ways to determine if two triangles are similar: The first is to measure the corresponding angles; if the corresponding angles are equal then the triangles are similar The second way is to look at the corresponding sides, if the corresponding sides are in a proportionate ratio the triangles are similar This side of Triangle A measures 3 inches, the corresponding side on Triangle B measures 9 inches, the ratio is 3/9 or in lowest terms 1/3 This side of triangle A measures 5 inches, the corresponding side on Triangle B measures 15 inches, the ratio is 5/15 or in lowest terms 1/3 This side of Triangle A measures 4 inches, the corresponding side on Triangle B measures 12 inches, the ratio is 4/12 or in lowest terms 1/3 All corresponding sides have the same ratio, so the triangles are similar 5 11. ________________ is when figures have the same size and shape These figures are all identical in size and shape so these figures are congruent 12. There are three rules that you can use to prove that two triangles are congruent 1) ____‐_____‐_____ Rule: it states that if two sides and the angle formed by the two sides (this is called the ___________ Angle) of one triangle are congruent to the corresponding sides and contained angle of another triangle, then the two triangles are congruent Line segment AC and line segment EF are the same length and are therefore congruent Line segment BC and line segment GF are also the same length and therefore congruent The contained angles, angle ACB and angle EFG are the same size So using the side‐angle‐side rule, these two triangles are congruent 2) _____‐____‐_____ Rule: it states that if two angles and the side between them (this is called the __________ Side) are congruent to the corresponding two angles and the contained side of another triangle, then the two triangles are congruent Angle ACB and angle EFG are the same size Angle BAC and angle FEG are the same size The contained sides, line segment AC and line segment EF are the same length So using the angle‐side‐angle rule, these two triangles are congruent 3) ______‐_____‐_______ Rule: it states that if the three sides of a triangle are congruent to the three corresponding sides of another triangle, then the two triangles are congruent Line segment AC is congruent to line segment EF Line segment AB is congruent to line segment EG Line segment BC is congruent to line segment FG So using the side‐side‐side rule, these two angles are congruent 13. Geometry that describes the movement of congruent figures is called _____________Geometry 6 In motion geometry a figure can _______ to create a congruent image All points on the slide image are the same distance from the matching points on the original image The ____________________ shows the direction of the slide motion The direction of the slide can be up, down, left, or right This image has moved down two spaces and to the right six spaces The rule that describes the motion of the slide is D2; R6 A figure can _______ to create a congruent image All points in the flip image are the same distance from the flip line as the original figure but on the opposite side of the line A figure can also _______ to create a congruent image All points on the turn image are turned on the same angle from the same point called the_______________ Turns are measured as ¼ turns, ½ turns, ¾ turns and full turns A figure can turn in a _____________direction (cw), the same direction as the hands on a clock or in a __________________direction (ccw), the opposite direction as a clock Any figure that fits onto itself in less than full turn has ____________Symmetry or _________Symmetry 7 If I turn this square one quarter turn clockwise the turn image perfectly maps to the original square If I turn it ½ turn the turn image maps again It maps again with a ¾ turn and with a full turn The square maps onto itself 4 times in one full turn The square’s________________________, the number of times it maps on itself is 4 Here’s another example using an equilateral triangle How many times with the triangle map on itself within one full turn An equilateral triangle’s order of rotational symmetry is 3 8