B D A C Conjecture: m  B = 2(m  A) 7.

A B C D E 30  x 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 

A C B D 63 

A C B D 63   104

A C B D 63  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. 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 # 6 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.

C D F A E B Outline of proof: 1.  A   B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) From HW # 6 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.

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 # 6 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.

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 4.  ADE   BFE (AAS) From HW # 6 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.

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 4.  ADE   BFE (AAS) 5. DE  EF and AD  BF (CPCTC) From HW # 6 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.

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 4.  ADE   BFE (AAS) 5. DE  EF and AD  BF (CPCTC) 6.  DEF is isosceles (definition of isosceles  ) From HW # 6 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.

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 4.  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 # 6 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.

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 4.  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 # 6 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.

6. Think about how you would prove that the altitudes to the legs of an isosceles triangle are congruent. From HW # 6

B D A C Conjecture: m  B = 2(m  A) 7.

Use Geometer’s Sketchpad to construct quadrilateral ABCD in which AB is parallel to CD and BC is parallel to AD.

Quadrilaterals

A rhombus is a parallelogram with one pair of adjacent sides congruent. A rectangle is a parallelogram with one right angle. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A square is a rhombus and a rectangle. Definitions

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. bases legs Base angles (there are two pairs)

ParallelogramRhombusRectangleSquareTrapezoidIsosceles 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.