6.2: Isosceles Triangles
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1 6.2: Isosceles Triangles Dec 5 4:34 PM 1
2 Define an Isosceles Triangle. A triangle that has (at least) two sides of equal length. Dec 5 4:34 PM 2
3 Draw an Isosceles Triangle. Label all parts and mark the parts of congruency. On your drawing above, identify the vertex, base and base angles. Vertex Base Angle BASE Base Angle Dec 5 4:34 PM 3
4 What is true about the base angles of an Isosceles triangle? They re congruent! Define Isosceles Triangle Base Angles Theorem: If a triangle has 2 sides then, the angles opposite them are Dec 5 4:36 PM 4
5 Define Isosceles Triangle Symmetry Theorem: The line containing the angle bisector of the Vertex angle of an isosceles triangle is a Line of symmetry for the triangle. Vertex Angle Bisector Line of Symmetry Dec 6 10:05 AM 5
6 Define Isosceles Triangle Coincidence Theorem: In an isosceles triangle, the angle bisector of the vertex, the median from the vertex, the perpendicular bisector of the base, and Line of symmetry, are all the same. Dec 6 10:11 AM 6
7 Draw a circle with center w. Put points a & b on the circle. Draw radii wa and wb. Explain why the triangle you just created is isosceles. A Triangle is isosceles because W B AW=WB by definition of a Circle Therefore two sides are congruent length! Dec 6 10:13 AM 7
8 What is segment AB called? A A chord of circle W W B Dec 6 10:13 AM 8
9 Oct 13 1:42 PM 9
10 Oct 13 1:44 PM 10
11 Angle 1 and 3 are vert. angles Def. Vert. angles Angle 2 and 4 are vert. angles Def. Vert. angles Oct 13 1:45 PM 11
12 Conclusion Justification Dec 6 10:20 AM 12
13 Conclusion Justification PQR is isosceles Given With PQ = QR. Dec 6 10:20 AM 13
14 Conclusion Justification PQR is isosceles With PQ = QR. Given Isosceles Triangle Base Angles Theorem Dec 6 10:20 AM 14
15 Conclusion Justification PQR is isosceles With PQ = QR. Given Isosceles Triangle Base Angles Theorem Vertical Angle Theorem Dec 6 10:20 AM 15
16 Conclusion Justification PQR is isosceles Given With PQ = QR. Isosceles Triangle Base Angles Theorem Vertical Angle Theorem Transitive Property of = Dec 6 10:20 AM 16
17 What is the sum of a triangle? = m<x + m<z 157 = m<x + m<z 157 = 2 m<x /2 = m<x 78.5 = m<x Dec 6 10:20 AM 17
18 Dec 6 10:24 AM 18
19 Conclusion Justification Given Dec 6 10:24 AM 19
20 Conclusion Justification Given Given Dec 6 10:24 AM 20
21 Conclusion Justification Given Given 3. Isosceles Triangle Base Angles Theorem Dec 6 10:24 AM 21
22 Conclusion Justification Given Given Isosceles Triangle Base Angles Theorem Isosceles Triangle Base Angles Theorem Dec 6 10:24 AM 22
23 Conclusion Justification Given Given Isosceles Triangle Base Angles Theorem Isosceles Triangle Base Angles Theorem Vertical Angle Theorem 6. Dec 6 10:24 AM 23
24 Conclusion Justification Given Given Isosceles Triangle Base Angles Theorem Isosceles Triangle Base Angles Theorem Vertical Angle Theorem Transitive Prop of Dec 6 10:24 AM 24
25 Define Equilateral Triangle Symmetry Theorem: Every equilateral triangle has 3 symmetry lines, which are the bisectors of the angles. Dec 6 10:38 AM 25
26 Oct 13 1:45 PM 26
27 Oct 16 7:56 AM 27
28 A E the measure of angle EAC is o Oct 16 7:58 AM 28
29 What is the degree measure of each angle of an equilateral triangle? 60 degrees Therefore an equilateral triangle is also called an equiangular triangle. How many lines of symmetry does an isosceles triangle have? 1 line of symmetry How many lines of symmetry does an equilateral triangle have? 3 lines of symmetry Is an isosceles triangle equilateral? NO (only two sides congruent) Is an equilateral triangle isosceles? YES (at least two sides are congruent) Dec 6 10:43 AM 29
30 Oct 20 10:24 PM 30
31 Oct 20 10:25 PM 31
32 Oct 20 10:25 PM 32
33 Oct 20 10:25 PM 33
34 Conclusion Justification Oct 20 10:26 PM 34
35 Oct 20 10:26 PM 35
36 Oct 20 10:26 PM 36
37 Oct 20 10:27 PM 37
38 Oct 20 10:27 PM 38
39 Oct 20 10:27 PM 39
40 Oct 20 10:28 PM 40
41 Conclusion Justification Oct 20 10:28 PM 41
42 Oct 20 10:28 PM 42
43 Oct 20 10:29 PM 43
44 Oct 20 10:29 PM 44
45 Oct 20 10:29 PM 45
46 Oct 20 10:29 PM 46
47 Oct 20 10:29 PM 47
48 Oct 20 10:30 PM 48
49 Oct 20 10:30 PM 49
50 Oct 20 10:32 PM 50
51 Oct 11 12:45 PM 51
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