1. 34a 15 2. 2 3. z = 139 4. n = 2 5. angle: degrees x = 28 6. right isosceles 7. angle: degrees x = 6 Monday HW Answers. 1
Recap! A straight angle measures. A triangle always measures. A quadrilateral measures. Congruent means: Supplementary angles measure. Complementary angles measure. Adjacent angles are share a common. Vertical Angles are and. 2
Recap! 3
Recap! PRACTICE: Identify each triangle by both side and angle isosceles acute right, scalene equilateral, equilangular right, scalene isosceles, acute isosceles, obtuse 4
` Using a Protractor Watch the following video to review how to use a protractor. (https://www.youtube.com/watch?v=ebsa_1cpn9s) Steps for using a Protractor: 1. First draw the, base which is a straight 2. Line up your protractor in the corner of the base with the center dot of the protractor. 3. Locate the degree in which you are trying to measure. Mark this with a dot. 4. Draw a line from the base through the dot you created. It does not matter how long you draw this line. 5. Repeat these steps from the line you just created for your second angle. 6. Always measure the last angle to ensure you drew it correctly. line 5
Protractor Practice: Create a triangle with angles that measure 5, 25, and 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 step 1: draw a base (straight line) step 2: line up the center dot of protractor to the corner of the base. step 3: Identify the degree you are searching for with a dot. step 4: connect to the base through your dot. step 5: place the protractor in the opposite corner of the base. step 6: identify your second angle measurement with a dot. step 7: draw a line from the base through your dot until the 2 lines connect to form your triangle ***DON'T FORGET TO LABEL EACH ANGLE AS YOU DRAW IT! 6
Protractor Practice: Create a triangle with angles that measure 65, 75, and 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 step 1: draw a base (straight line) step 2: line up the center dot of protractor to the corner of the base. step 3: Identify the degree you are searching for with a dot. step 4: connect to the base through your dot. step 5: place the protractor in the opposite corner of the base. step 6: identify your second angle measurement with a dot. step 7: draw a line from the base through your dot until the 2 lines connect to form your triangle ***DON'T FORGET TO LABEL EACH ANGLE AS YOU DRAW IT! 7
Warm Up: Wednesday April 11th 1. If the perimeter is 47, find x and the lengths of the three sides then classify the triangle. perimeter = side 1 + 2 + 3 p = 2x+6 + 3x+8 + x+3 47 = 6x + 17 (combined like terms) USE SUBSTITUTION = 6x (got rid of addition) 2x+6 > 2(5) + 6 = 16 3x+8 > 3(5) + 8 = 23 5 = x (got rid of multiplication) x+3 > 5 + 3 = 8 2. What requirements do you need to determine if a triangle is possible? (think about shape/sides and angles) must have 3 sides and angles angles must add up to 1 degrees shape must be closed (lines connect) 2 smaller sides must be greater than the bigger (small + small > large) 8
1. 23c + 92 2. 143.75 3. k = 0 4. x = 2 5. x = 61 6. obtuse isosceles 7. x = 7 angles are 52 and 44 HW Answers Tuesday 9
1. 45x 42 2. 8.25 3. d = 2.18 4. m = 1 5. x = 35 6. yes 7. x = 7 angles are, HW Answers Wednesday
3 1 degrees greater than Triangle Inequality Theorem side angle side angle side angle unique angle angle side side side side angle angle angle 1 can form more than one possible triangle 11
Triangle Inequality Theorem https://www.youtube.com/watch?v=onr7wtdjhyk can be used to determine if a triangle is possible based on the given side lengths can be used to predict the range of the length of the third side when given the measurement of two other side lengths. 12
Triangle Inequality Theorem Examples Small + Small > Large 3 + 7 > 8 > 8 True. Does form a triangle 3 + 6 > 9 > False. Does not form a triangle 13
Triangle Inequality Theorem Examples If you are predicting the length of the third side given 2 prior measurements you must find a range. > This is because you do not know if you are given the 2 shorter lengths of if you are given the larger side. You could be searching for either or. > Your final answer will be written in the form of an inequality. Small + Small > Large Example: A triangle has sides of lengths 8cm and cm. Describe the lengths possible for the third side. (Let x represent the length of the third side) You do not know if x is larger than or smaller than 8. Therefor, you must solve 2 ways. For both the smaller side and the larger. x + 8 > 8 + > x 18 > X x > 2 or X < 18 x must be greater than 2 but less 18 2 < X < 18 This range shows that x is between the 2 numbers 14
Triangle Inequality Theorem Practice Determine if a triangle with the following side lengths possible? 1. 6,, 4 2. 12, 17, 3. 19, 7, 12 Use the information to predict the third length of the given triangle with side lengths of 25, 13 and x. 15
1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 constructions steps primary end point 0 1 1 1 1 draw a base,measure your angle from the center dot of the protractor in the left corner, followed by the another angle in the right corner. Extend your lines till they connect. Always label your angles. 1 0 0 0 1 1 1 1 0 1 The longest length is always the slant. Measure a 3 cm base first, a height of 4 cm, connect the top of the height to the tip of your base. Measure it to make sure that it is 5 cm. 2 sentences minimum explaining why #1 is not unique but #2 is 16
no unique 45 + 45 + 1 1 1 1 1 0 0 0 1 1 1 1 complete on your own 0 1 it is a triangle because the angles add up to 1 degrees and the lines connect when drawn. It is more than one becuase AAA is not a unique triangle since the side lengths can vary. 0 1 15 5 13 14 12 4 11 0 0 31 1 2 1 3 3 cm 4 2 5 6 2 cm 7 3 8 9 SSS is in our list of unique triangles. Only one possibility can be formed for side lengths and angles given this information. complete on your own (YES, you must actually do this! 3 sentences minimum!!!) 17