FeatureLesson Geometry Lesson Main In GHI, R, S, and T are midpoints. 1. Name all the pairs of...
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Transcript of FeatureLesson Geometry Lesson Main In GHI, R, S, and T are midpoints. 1. Name all the pairs of...
FeatureLesson
GeometryGeometry
LessonMain
In GHI, R, S, and T are midpoints.
1. Name all the pairs of parallel segments.
2. If GH = 20 and HI = 18, find RT.
3. If RH = 7 and RS = 5, find ST.
4. If m G = 60 and m I = 70, find m GTR.
5. If m H = 50 and m I = 66, find m ITS.
6. If m G = m H = m I and RT = 15, find the perimeter of GHI.
RT || HI, RS || GI, ST || HG
90
64
70
7
9
Lesson 5-1 Quiz – Midsegments of Triangles
5-1
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
5-2
When a point is the same distance from two or moreobjects, the point is said to be equidistant fromthe objects. Triangle congruence theorems can beused to prove theorems about equidistant points.
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
5-2
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
5-2
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
5-2
The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line.
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
5-2
FeatureLesson
GeometryGeometry
LessonMain
Use the map of Washington, D.C. Describe the set of points
that are equidistant from the Lincoln Memorial and the Capitol.
The Converse of the Perpendicular Bisector Theorem states If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
Quick Check
Additional Examples
5-2
Real-World Connection
FeatureLesson
GeometryGeometry
LessonMain
(continued)
A point that is equidistant from the Lincoln Memorial and the Capitol
must be on the perpendicular bisector of the segment whose
endpoints are the Lincoln Memorial and the Capitol.
Therefore, all points on the perpendicular bisector of the segment
whose endpoints are the Lincoln Memorial and the Capitol are
equidistant from the Lincoln Memorial and the Capitol.
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
Additional Examples
5-2
Quick Check
FeatureLesson
GeometryGeometry
LessonMain
Find x, FB, and FD in the diagram above.
FD = FB Angle Bisector Theorem
7x – 37 = 2x + 5 Substitute.
7x = 2x + 42 Add 37 to each side.
5x = 42 Subtract 2x from each side.
x = 8.4 Divide each side by 5.
FB = 2(8.4) + 5 = 21.8 Substitute.
FD = 7(8.4) – 37 = 21.8 Substitute.
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
Additional Examples
5-2
Using the Angle Bisector Theorem
Quick Check
FeatureLesson
GeometryGeometry
LessonMain
Use this figure for Exercises 1–3.
1. Find BD.
2. Complete the statement: C is equidistant from ? .
3. Can you conclude that CN = DN? Explain.
Use this figure for Exercises 4–6.
4. Find the value of x.
5. Find CG.
6. Find the perimeter of quadrilateral ABCG.
6
Lesson 5-2
points A and B
16
48
8
No; if CN = DN, CNB DNB by SAS and CB = DB by CPCTC, whichis false.
Bisectors in TrianglesBisectors in Triangles
Lesson Quiz
5-2
FeatureLesson
GeometryGeometry
LessonMain
(For help, go to Lesson 1-7.)
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
1. Draw a triangle, XYZ. Construct STV so that STV XYZ.
2. Draw acute P. Construct Q so that
3. Draw AB. Construct a line CD so that CD AB and CD bisects AB. 4. Draw acute angle E. Construct the bisector of E.
TM bisects STU so that m STM = 5x + 4 and m MTU = 6x – 2.
5. Find the value of x.
6. Find m STU.
Use a compass and a straightedge for the following.
Check Skills You’ll Need
Q P.
Check Skills You’ll Need
5-2
FeatureLesson
GeometryGeometry
LessonMain
Lesson 5-2
Bisectors in TrianglesBisectors in Triangles
Solutions
1. 2.
3. 4.
5. Since TM bisects STU, m STM = m MTU. So, 5x + 4 = 6x – 2. Subtract 5x from both sides: 4 = x – 2; add 2 to both sides: x = 6.
6. From Exercise 5, x = 6. m STU = m STM + m MTU = 5x + 4 + 6x – 2 = 11x + 2 = 11(6) + 2 = 68.
1-4. Answers may vary. Samples given:
Check Skills You’ll Need
5-2