4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is...
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Transcript of 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is...
![Page 1: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/1.jpg)
4.7 – Isosceles Triangles
GeometryMs. Rinaldi
![Page 2: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/2.jpg)
Isosceles Triangles
• Remember that a triangle is isosceles if it has at least two congruent sides.
• When an isosceles triangle has exactly two congruent sides, these two sides are the legs.
• The angle formed by the legs is the vertex angle.
• The third side is the base of the isosceles triangle.
• The two angles adjacent to the base are called base angles.
![Page 3: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/3.jpg)
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If , thenACAB CB
![Page 4: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/4.jpg)
Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If , thenCB ACAB
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EXAMPLE 1 Apply the Base Angles Theorem
SOLUTION
In DEF, DE DF . Name two congruent angles.
DE DF , so by the Base Angles Theorem, E F.
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EXAMPLE 2 Apply the Base Angles Theorem
In . Name two congruent angles.QRPQPQR ,
P
RQ
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EXAMPLE 3 Apply the Base Angles Theorem
Copy and complete the statement.
1. If HG HK , then ? ? .
If KHJ KJH, then ? ? .If KHJ KJH, then ? ? .2. 2.
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EXAMPLE 4 Apply the Base Angles Theorem
P
R
Q
(30)°
Find the measures of the angles.
SOLUTION
Since a triangle has 180°, 180 – 30 = 150° for the other two angles.
Since the opposite sides are congruent, angles Q and P must be congruent.
150/2 = 75° each.
![Page 9: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/9.jpg)
EXAMPLE 5 Apply the Base Angles Theorem
P
R
Q
(48)°
Find the measures of the angles.
![Page 10: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/10.jpg)
EXAMPLE 6 Apply the Base Angles Theorem
P
R
Q(62)°
Find the measures of the angles.
![Page 11: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/11.jpg)
EXAMPLE 7 Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle.
P
RQ(20x-4)°
(12x+20)°
SOLUTION
Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4
20 = 8x – 4
24 = 8x
3 = xPlugging back in,
And since there must be 180 degrees in the triangle,
564)3(20
5620)3(12
Rm
Pm
685656180Qm
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EXAMPLE 8 Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle.
P
R
Q(11x+8)° (5x+50)°
![Page 13: 4.7 – Isosceles Triangles Geometry Ms. Rinaldi. Isosceles Triangles Remember that a triangle is isosceles if it has at least two congruent sides. When.](https://reader037.fdocuments.us/reader037/viewer/2022110403/56649e745503460f94b73eee/html5/thumbnails/13.jpg)
EXAMPLE 9 Apply the Base Angles Theorem
Find the value of x. Then find the length of the labeled sides.
P
R
Q(80)° (80)°
SOLUTION
Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 7x = 3x + 40
4x = 40
x = 107x 3x+40
Plugging back in,
QR = 7(10)= 70PR = 3(10) + 40 = 70
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EXAMPLE 10 Apply the Base Angles Theorem
Find the value of x. Then find the length of the labeled sides.
P
RQ
(50)°
(50)°
10x – 2
5x+3