MIDLINE THEOREM.pptx
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The document discusses the midline theorem in geometry. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. Several examples are provided to demonstrate using the theorem to solve for unknown side lengths of triangles.
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What is the missing reason in the proof Given with diagonal .docx
What is the missing reason in the proof?
Given: with diagonal
Prove:
Statements
Reasons
1.
1. Definition of parallelogram
2.
2. Alternate Interior Angles Theorem
3.
3. Definition of parallelogram
4.
4. Alternate Interior Angles Theorem
5.
5. ?
6.
6. ASA
A. Reflexive Property of Congruence
B. Alternate Interior Angles Theorem
C. ASA
D. Definition of parallelogram
Find the values of a and b. The diagram is not to scale.
A.
B.
C.
D.
Complete this statement: A polygon with all sides the same length is said to be ____.
A. regular
B. equilateral
C. equiangular
D. convex
Which statement is true?
A. All squares are rectangles.
B. All quadrilaterals are rectangles.
C. All parallelograms are rectangles.
D. All rectangles are squares.
What is LM?
A. 176
B. 98
C. 88
D. 32
Which description does NOT guarantee that a trapezoid is isosceles?
A. congruent bases
B. congruent legs
C. both pairs of base angles congruent
D. congruent diagonals
Which description does NOT guarantee that a quadrilateral is a square?
A. has all sides congruent and all angles congruent
B. is a parallelogram with perpendicular diagonals
C. has all right angles and has all sides congruent
D. is both a rectangle and a rhombus
Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?
A.
B.
C.
D.
and Find
The diagram is not to scale.
A. 60
B. 10
C. 110
D. 20
WXYZ is a parallelogram. Name an angle congruent to
A.
B.
C.
D.
The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.
A.
B.
C.
D.
Which Venn diagram is NOT correct?
A.
B.
C.
D.
Classify the figure in as many ways as possible.
A. rectangle, square, quadrilateral, parallelogram, rhombus
B. rectangle, square, parallelogram
C. rhombus, quadrilateral, square
D. square, rectangle, quadrilateral
In the rhombus, Angle 1 = 140. What are Angles 2 and 3?
The diagram is not to scale.
A. Angle 2 = 40 and Angle 3 = 70
B. Angle 2 = 140 and Angle 3 = 70
C. Angle 2 = 40 and Angle 3 = 20
D. Angle 2 = 140 and Angle 3 = 20
Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex.
A. cannot tell
B. less than
C. greater than
D. equal to
Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length.
A. Arrange four equal-length sides so the diagonals bisect each other.
B. Arrange four equal-length sides so the diagonals are equal lengths also.
C. Make each diagonal the same length as four equal-length sides.
D. Not possible; Lucinda has to be able to measure a right angle.
Whi.
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- 2. Midline Theorem The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half as long.
- 3. Midline Theorem Midline is equal to one half of the base of a triangle. A D E B C DE= 𝟏 𝟐 (𝑨𝑩)
- 4. 1. If DE = 10.5 cm , What is AB? A D E B C EXAMPLES!!!
- 5. 1. If DE = 10.5 cm , What is AB? Answer: AB = 21 cm A D E B C 10.5= 𝟏 𝟐 (𝑨𝑩) EXAMPLES!!!
- 6. 2. If BC= 32 cm , What is CE? A D E B C EXAMPLES!!!
- 7. 2. If BC= 32 cm , What is CE? Answer: CE = 16 cm A D E B C EXAMPLES!!!
- 8. 3. If AB = 30 cm, What is DE? A D E B C EXAMPLES!!!
- 9. 3. If AB = 30 cm, What is DE? A D E B C DE= 𝟏 𝟐 (𝑨𝑩) DE= 𝟏 𝟐 (𝟑𝟎) DE= 15 cm EXAMPLES!!!
- 10. 4. DE= (3x – 2) cm and AB = (9x – 13) cm, solve for x. A D E B C EXAMPLES!!!
- 11. 4. DE= (3x – 2) cm and AB = (9x – 13) cm, solve for x. A D E B C DE= 𝟏 𝟐 (𝑨𝑩) 3x – 2 = 𝟏 𝟐 (𝟗𝒙 − 𝟏𝟑) 6x – 4 = 𝟗𝒙 − 𝟏𝟑 6x – 9x = −𝟏𝟑 + 𝟒 – 3x = −𝟗 x = 𝟑 EXAMPLES!!!
- 12. 4. DE= (3x – 2) cm and AB = (9x – 13) cm, solve for x. x = 𝟑 AB = (9x – 13) cm DE= (3x – 2) cm
- 13. 4. DE= (3x – 2) cm and AB = (9x – 13) cm, solve for x. DE = 3x – 2 x = 𝟑 DE = 3(3) – 2 DE = 7 cm AB = (9x – 13) cm AB = 9x – 13 AB = 9(3) – 13 AB = 14 cm DE= (3x – 2) cm
- 14. “Alldreamsarewithin reach.All youhave to dois keep movingtowardsthem”. -Viola Davis-