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1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Date: Aim: What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems? Name: Launch: Directions: Find each missing measure. 2. 1. K Isosceles Triangle Theorm m/J = 68° m/K= 44° 168 68° ● Same L 1 68 +68 136 B 9.5=45 +2 47 Isosceles Triangle Theorem Converse of Isosceles Triangle Theorem 7 180 - 136 44 47 3 15/40+800 10 ● Parts of an Isosceles Triangle: • The two congruent sides are called legs. The angle where the sides intersect is called the vertex angle. The side opposite the vertex angle is called the base. • The angles along the base are called base angles. 12 cm X<77° R 47 26 9x+2 Y 186 -154 26 86 +77 154 YZ = m/Y= 26° ISOSCELES TRIANGLES 17X+1 10 A Conv Converse of Isosceles trangle 12cm Example: If AB CB, then LA = LC 13x-18 47 A S 3. 9 ft Acute triangle 60° legs 9x+2 = 13x-18 -2 -2 9x = 13x-20 -13x -13x - 4x = -20 -4 -4 B Mini Lesson: 4. In ARST, if RT = ST, m/R = 9x + 2, m≤S = 13x - 18, and m/T = 17x + 1, find x and the measure of each angle. T 60° If two sides of a triangle are congruent, then the angles opposite those sides are congruent. + Example: If A2 <C, then AB = CB EQUILATERAL TRIANGLES A triangle is equilateral if and only if it is equiangular! If mA = m/B = m/C, then AB=BC=AC If AB = BC = AC, then MLA MLB MLC ·១ If two angles of a triangle are congruent, then the sides opposite those angles are congruent. X=5 60 base angle base m/C= BC...
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Alternative transcript:
= 9 AC = 2 с B Vertex angle legs 86 47 +47 180 Converse of Isoscels 3 60° aft aft C 0000 0000 0000 x =_5 m/R = 47 m/S= 47 mZT= 86 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Workshop: Directions: Find each missing measure. 6. (4x + 7)° 4-8=32 +7 39 D 39 4x+7 = qx -33 -7 -7 4 x = 9x - 40 -9x - 9x 28 7x-35 9.8 = z" 33 39 -5x = -40 亏亏 Obtuse triangle W 126 -48 78 102 (9x-33)° F X-H |x=8 x+b 24 13 JK = KL = JL 23=2K = LL : 1 39 ++39 Y 39 78 78 16 -78 4X-8 28 7x-48 7.10 102 7.9=13 -35 78 5x-12 5 13 4 18 -5 40 28 E 7. 14.9 286' 28 74° 16 9x - 73 71 剛 -73 11 9+4 5. Acute Angle 9. In ADEF, if ZD = ZE, DE = x + 4, EF = 4x - 8, and DF = 7x - 35, find x and the measure of each side. 74° Nº -5x -5x 24 7x - 48 = 5x - 12 +48 +48 2 x = 36 2 2 7x = 5x +36 32 | 3x + 23 | 1 24 cm K | x=16| 16 7x-35 = 4x -8 +35 +35 23 7x = 4x + 27 -4x -4x 3x - 27 3 3 18 2 36 |x=18| 24 10. In AWXY, if WX = WY, m/W = x + 6, mZX = 5x − 12, and mZY = 7x - 48, find x and the measure of each angle. 8 10 5 L 16 4 +74 148 9x-73 = 3x+23 +73 +73 mLJ = 2L m∠K = 24 mLL = 2- 6x 7,10 -48 9x = 3x+96 |x=q -3x-3x 32 o -12 = 96 下 9 x= DE = 13 EF = 28 DF = _28 78 x = 18 m<W = 24 m<X = _78 mZY = _78 5 16 144 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Name: Directions: Find each missing measure. 1. S 3. 54° 39 4x + 23 5. 60 +60 7x + 19 T 120 72 60° 7.10 180 -108 78° 72 Directions: Find the value of each variable and all missing angles. 4. 24 180 -120 78° 60° 180 -156 60 7,10 39 10x - 1 Date: Homework ** This is a 2-page document! ** U 24 1 78 +78 156 24 Acute Isosceles trangle Acute equilateral triangle 8 54 + 54 108 m/T = 72 m/U= 54 4x+23 = 10x-1 - 23 -23 4x=10X-24 -10x -10x -6x=-24 - - 27 4 108 -8√ 28 -28 11x-89 7x+19=11x-89 -19 -19 -1|x-1|x X=4 7x=11x-108 -4x=-108 -4 -4 16 +23 39 2. 60 6. 60 (4x + 8)° 60 29° 60 13 60 +8 60 122 (11x - 65)° 11x-65=122 +65 +65 R Ilx = 187 11 11 60 60 +60 60 60 + 60 180 Acute scalene trangle 180 4x+8 +4x+8+4x+8 = 180 12x+24=180 -24 -24 12x=156 29 m/P = 60 m20= 60 mZR = 60 – ? 10 X=13 -58 122 29 +29 2 58 X=17 This is obtuse isosceles 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles 7. If AABC is an isosceles triangle and ADBE is an equilateral triangle, find each missing measure. (4x + 3)°, A 4x+3=9x-47 -3 K -3 4x = 9x-50 -9x -9x 143 -5x = -50 -5 -5 3x+18 68 3x+23 120 3 75 D x=10 960 7x-58 43 +43=86 9x-40 180 -60 B 30 2x-8 53 5 60 45 126 68 7x-37 86 -60 3 6788 E 120 26 L 7x-58-3x+18 +58 15 -7 910515 -37 68 8. In AABC, if AC = CB, mZA = 3x + 18, m/B = 7x - 58, and m/C= 2x - 8, find x and the measure of each angle. 4x=76 4 4 8 +58 7x = 3x+7b -3x -3x -47 120 +43 تفاق 163 13 5 (9x - 47)° C ID 43 19 .3 A с 157 †18 75 9. In AKLM, if ZK = ZL, KL = 9x - 40, LM = 7x-37, and KM = 3x + 23, find x and the measure of each side. 3x +23-7x-37 M -23 1 188 -163 X=19 7.10 ali i /io- -23 - 4x=-60 -4 -4 135 -40 95 17 3x=7x-60 -7x-7x 133 m/1 = 43 17 m2 = m23 = -120 m24 = 60 m25= 60 m26 = m27 = m28 = 120 m/9 = 43 60 17 x =_19 x=15 mZA = mZB = m/C= 30 x = KL = LM = KM = 75 75 9.5 68 68 95 68 +68 180
What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems?
What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems?
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1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Date: Aim: What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems? Name: Launch: Directions: Find each missing measure. 2. 1. K Isosceles Triangle Theorm m/J = 68° m/K= 44° 168 68° ● Same L 1 68 +68 136 B 9.5=45 +2 47 Isosceles Triangle Theorem Converse of Isosceles Triangle Theorem 7 180 - 136 44 47 3 15/40+800 10 ● Parts of an Isosceles Triangle: • The two congruent sides are called legs. The angle where the sides intersect is called the vertex angle. The side opposite the vertex angle is called the base. • The angles along the base are called base angles. 12 cm X<77° R 47 26 9x+2 Y 186 -154 26 86 +77 154 YZ = m/Y= 26° ISOSCELES TRIANGLES 17X+1 10 A Conv Converse of Isosceles trangle 12cm Example: If AB CB, then LA = LC 13x-18 47 A S 3. 9 ft Acute triangle 60° legs 9x+2 = 13x-18 -2 -2 9x = 13x-20 -13x -13x - 4x = -20 -4 -4 B Mini Lesson: 4. In ARST, if RT = ST, m/R = 9x + 2, m≤S = 13x - 18, and m/T = 17x + 1, find x and the measure of each angle. T 60° If two sides of a triangle are congruent, then the angles opposite those sides are congruent. + Example: If A2 <C, then AB = CB EQUILATERAL TRIANGLES A triangle is equilateral if and only if it is equiangular! If mA = m/B = m/C, then AB=BC=AC If AB = BC = AC, then MLA MLB MLC ·១ If two angles of a triangle are congruent, then the sides opposite those angles are congruent. X=5 60 base angle base m/C= BC...
1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Date: Aim: What are the properties of isosceles and equilateral triangles? How can we use these properties to solve missing angle or missing side problems? Name: Launch: Directions: Find each missing measure. 2. 1. K Isosceles Triangle Theorm m/J = 68° m/K= 44° 168 68° ● Same L 1 68 +68 136 B 9.5=45 +2 47 Isosceles Triangle Theorem Converse of Isosceles Triangle Theorem 7 180 - 136 44 47 3 15/40+800 10 ● Parts of an Isosceles Triangle: • The two congruent sides are called legs. The angle where the sides intersect is called the vertex angle. The side opposite the vertex angle is called the base. • The angles along the base are called base angles. 12 cm X<77° R 47 26 9x+2 Y 186 -154 26 86 +77 154 YZ = m/Y= 26° ISOSCELES TRIANGLES 17X+1 10 A Conv Converse of Isosceles trangle 12cm Example: If AB CB, then LA = LC 13x-18 47 A S 3. 9 ft Acute triangle 60° legs 9x+2 = 13x-18 -2 -2 9x = 13x-20 -13x -13x - 4x = -20 -4 -4 B Mini Lesson: 4. In ARST, if RT = ST, m/R = 9x + 2, m≤S = 13x - 18, and m/T = 17x + 1, find x and the measure of each angle. T 60° If two sides of a triangle are congruent, then the angles opposite those sides are congruent. + Example: If A2 <C, then AB = CB EQUILATERAL TRIANGLES A triangle is equilateral if and only if it is equiangular! If mA = m/B = m/C, then AB=BC=AC If AB = BC = AC, then MLA MLB MLC ·១ If two angles of a triangle are congruent, then the sides opposite those angles are congruent. X=5 60 base angle base m/C= BC...
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Knowunity is the # 1 ranked education app in five European countries
Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.
Still not sure? Look at what your fellow peers are saying...
iOS User
I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D
Stefan S, iOS User
The application is very simple and well designed. So far I have found what I was looking for :D
SuSSan, iOS User
Love this App ❤️, I use it basically all the time whenever I'm studying
Alternative transcript:
= 9 AC = 2 с B Vertex angle legs 86 47 +47 180 Converse of Isoscels 3 60° aft aft C 0000 0000 0000 x =_5 m/R = 47 m/S= 47 mZT= 86 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Workshop: Directions: Find each missing measure. 6. (4x + 7)° 4-8=32 +7 39 D 39 4x+7 = qx -33 -7 -7 4 x = 9x - 40 -9x - 9x 28 7x-35 9.8 = z" 33 39 -5x = -40 亏亏 Obtuse triangle W 126 -48 78 102 (9x-33)° F X-H |x=8 x+b 24 13 JK = KL = JL 23=2K = LL : 1 39 ++39 Y 39 78 78 16 -78 4X-8 28 7x-48 7.10 102 7.9=13 -35 78 5x-12 5 13 4 18 -5 40 28 E 7. 14.9 286' 28 74° 16 9x - 73 71 剛 -73 11 9+4 5. Acute Angle 9. In ADEF, if ZD = ZE, DE = x + 4, EF = 4x - 8, and DF = 7x - 35, find x and the measure of each side. 74° Nº -5x -5x 24 7x - 48 = 5x - 12 +48 +48 2 x = 36 2 2 7x = 5x +36 32 | 3x + 23 | 1 24 cm K | x=16| 16 7x-35 = 4x -8 +35 +35 23 7x = 4x + 27 -4x -4x 3x - 27 3 3 18 2 36 |x=18| 24 10. In AWXY, if WX = WY, m/W = x + 6, mZX = 5x − 12, and mZY = 7x - 48, find x and the measure of each angle. 8 10 5 L 16 4 +74 148 9x-73 = 3x+23 +73 +73 mLJ = 2L m∠K = 24 mLL = 2- 6x 7,10 -48 9x = 3x+96 |x=q -3x-3x 32 o -12 = 96 下 9 x= DE = 13 EF = 28 DF = _28 78 x = 18 m<W = 24 m<X = _78 mZY = _78 5 16 144 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles Name: Directions: Find each missing measure. 1. S 3. 54° 39 4x + 23 5. 60 +60 7x + 19 T 120 72 60° 7.10 180 -108 78° 72 Directions: Find the value of each variable and all missing angles. 4. 24 180 -120 78° 60° 180 -156 60 7,10 39 10x - 1 Date: Homework ** This is a 2-page document! ** U 24 1 78 +78 156 24 Acute Isosceles trangle Acute equilateral triangle 8 54 + 54 108 m/T = 72 m/U= 54 4x+23 = 10x-1 - 23 -23 4x=10X-24 -10x -10x -6x=-24 - - 27 4 108 -8√ 28 -28 11x-89 7x+19=11x-89 -19 -19 -1|x-1|x X=4 7x=11x-108 -4x=-108 -4 -4 16 +23 39 2. 60 6. 60 (4x + 8)° 60 29° 60 13 60 +8 60 122 (11x - 65)° 11x-65=122 +65 +65 R Ilx = 187 11 11 60 60 +60 60 60 + 60 180 Acute scalene trangle 180 4x+8 +4x+8+4x+8 = 180 12x+24=180 -24 -24 12x=156 29 m/P = 60 m20= 60 mZR = 60 – ? 10 X=13 -58 122 29 +29 2 58 X=17 This is obtuse isosceles 1.2.6 ATA 4.3 Isosceles & Equilateral Triangles 7. If AABC is an isosceles triangle and ADBE is an equilateral triangle, find each missing measure. (4x + 3)°, A 4x+3=9x-47 -3 K -3 4x = 9x-50 -9x -9x 143 -5x = -50 -5 -5 3x+18 68 3x+23 120 3 75 D x=10 960 7x-58 43 +43=86 9x-40 180 -60 B 30 2x-8 53 5 60 45 126 68 7x-37 86 -60 3 6788 E 120 26 L 7x-58-3x+18 +58 15 -7 910515 -37 68 8. In AABC, if AC = CB, mZA = 3x + 18, m/B = 7x - 58, and m/C= 2x - 8, find x and the measure of each angle. 4x=76 4 4 8 +58 7x = 3x+7b -3x -3x -47 120 +43 تفاق 163 13 5 (9x - 47)° C ID 43 19 .3 A с 157 †18 75 9. In AKLM, if ZK = ZL, KL = 9x - 40, LM = 7x-37, and KM = 3x + 23, find x and the measure of each side. 3x +23-7x-37 M -23 1 188 -163 X=19 7.10 ali i /io- -23 - 4x=-60 -4 -4 135 -40 95 17 3x=7x-60 -7x-7x 133 m/1 = 43 17 m2 = m23 = -120 m24 = 60 m25= 60 m26 = m27 = m28 = 120 m/9 = 43 60 17 x =_19 x=15 mZA = mZB = m/C= 30 x = KL = LM = KM = 75 75 9.5 68 68 95 68 +68 180