conjecture: m b = 2(m a)
DESCRIPTION
7. Conjecture: m B = 2(m A). B. D. A. C. B. 30 . E. x. C. A. D. From HW # 6. Given:. 1. x = 15. Find the measure of the angle marked x. x. From HW # 6. x = 15. 2. A. D. B. C. 63 . 63. 41. 104. A. D. B. C. 63 . 63. 41. 104. A. D. B. C. 63 . . - PowerPoint PPT PresentationTRANSCRIPT
B
D
AC
Conjecture: mB = 2(mA)
7.
A
B
CD
E
30
x
BCAB
BEBD
1.
From HW # 6
Given:
x = 15
Find the measure of the angle marked x.
x
2.
x = 15
From HW # 6
A
C
B
D
63
63
41104
A
C
B
D
63
104
63
41
A
C
B
D
63
104
A
C
B
D
63
104 76
63
41
D
A B
C
D E F
14
5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
From HW # 6
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles4. ADE BFE (AAS)
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles4. ADE BFE (AAS)5. DE EF and AD BF (CPCTC)
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles4. ADE BFE (AAS)5. DE EF and AD BF (CPCTC)6. DEF is isosceles (definition of isosceles )
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles4. ADE BFE (AAS)5. DE EF and AD BF (CPCTC)6. DEF is isosceles (definition of isosceles ) 7. DC FC (subtraction post, AC – AD = BC – BF)
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
C
D F
A E B
Outline of proof:
1. A B (isosceles triangle theorem)2. AE EB (definition of midpoint)3. ADE and BFE are congruent right angles4. ADE BFE (AAS)5. DE EF and AD BF (CPCTC)6. DEF is isosceles (definition of isosceles ) 7. DC FC (subtraction post, AC – AD = BC – BF)8. CDF is isosceles.
From HW # 65. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles.
ABBCEF,ACED AB
D E
C
B
A
6. Think about how you would prove that the altitudes to the legs of an isosceles triangle are congruent.
From HW # 6
B
D
AC
Conjecture: mB = 2(mA)
7.
Use Geometer’s Sketchpad to construct quadrilateral ABCD in which AB is parallel to CD and BC is parallel to AD.
DC
B A
Quadrilaterals
DC
B A
A rhombus is a parallelogram with one pair of adjacent sides congruent.
DC
B A
A rectangle is a parallelogram with one right angle.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
DC
B A
DC
B A
A square is a rhombus and a rectangle.
Definitions
B A
C D
A trapezoid is a quadrilateral with exactly one pair of sides parallel.
An isosceles trapezoid is a trapezoid with the two non-parallel sides congruent.
B A
C D
bases
legs
Base angles (there are two pairs)
Parallelogram Rhombus Rectangle Square Trapezoid Isosceles Trapezoid
Exactly 1 pair of parallel sides
2 pairs of parallel sides
Exactly 1 pair of congruent sides
2 pairs of congruent sides
All sides congruent
Perpendicular diagonals
Congruent diagonals
Diagonals bisect angles
Diagonals bisect each other
Opposite angles congruent
Four right angles
Base angles congruent
HW #7
Fill in the chart (question 5) on the HW 7 handout.
Begin work on the rest of the problems.
You will have all period on Monday to complete it.