Isosceles Triangle Exploration
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This document discusses properties of an isosceles triangle with a perpendicular bisector. It notes that the perpendicular bisector bisects the triangle's congruent sides and concludes that the two triangles formed by the bisector are congruent. Therefore, their corresponding angles and sides are also congruent.
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Alternate angles: ∠BPQ and ∠DQP
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Geometry the congruence of triangles
The document discusses congruent triangles and different postulates that can be used to prove triangles are congruent. It states that triangles can be proved congruent without showing all three pairs of congruent sides and angles. It then provides examples of different postulates like AAS, SAS, and SSS that can be used to prove triangles congruent. It also discusses isosceles triangles and how if two isosceles triangles share a common base, the line segment joining their vertices will bisect the common base at a right angle.
Circlestangentchordtheorem
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11X1 T07 03 congruent triangles (2010)
The document discusses congruent triangles and the different tests that can be used to prove triangles are congruent. It states that in order to prove triangles are congruent, three pieces of information are required. It then lists and describes the four main tests: (1) Side-Side-Side, (2) Side-Angle-Side, (3) Angle-Angle-Side, and (4) Right Angle-Hypotenuse-Side. It provides an example proof using these tests and also defines different types of triangles like isosceles and equilateral triangles. Finally, it discusses some triangle terminology like altitude and median.
11 x1 t07 03 congruent triangles (2012)
The document discusses congruent triangles and the different tests that can be used to prove triangles are congruent. It states that in order to prove triangles are congruent, three pieces of information are required. It then lists and describes the four main tests: (1) Side-Side-Side, (2) Side-Angle-Side, (3) Angle-Angle-Side, and (4) Right Angle-Hypotenuse-Side. It provides an example proof using these tests and also defines different types of triangles like isosceles and equilateral triangles. Finally, it discusses some triangle terminology like altitude and median.
11X1 T08 03 congruent triangles (2011)
The document discusses congruent triangles and the different tests used to prove triangles are congruent. There are four tests: side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS). It also provides an example proof using AAS and SAS to show two sides of a quadrilateral are congruent. Finally, it defines isosceles and equilateral triangles.
Angles
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- Definition of Angles
- Parts of Angles
- Protractor
- Kinds of Angles
- Measuring Angles
The Assignment on the last slide is for them to have a background on the next lesson.
Presentation1
A quadrilateral is a shape with four sides, four angles, and four vertices. There are six types of quadrilaterals: trapezium, parallelogram, rectangle, rhombus, square, and kite. A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. The diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Opposite sides and opposite angles of a parallelogram are equal.
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Isosceles Triangle Exploration
- 1. Isosceles Triangle A B C
- 2. Isosceles Triangle with a Perpendicular Bisector A B C D
- 3. Isosceles Triangle with a Perpendicular Bisector A B C D
- 4. Isosceles Triangle with a Perpendicular Bisector Congruent side markings Perpendicular angle markings A B C D
- 5. Isosceles Triangle with a Perpendicular Bisector Congruent side markings Perpendicular angle markings What else do we know? A B C D
- 9. Isosceles Triangle with a Perpendicular Bisector If the two triangles are congruent, what else do we know? A B C D
- 10. Isosceles Triangle with a Perpendicular Bisector If the two triangles are congruent, what else do we know? <A = <C <BAD = <CAD All of its parts, angles and sides are congruent! A B C D
- 11. Isosceles Triangle with a Perpendicular Bisector A B C D You’ve used geometric reasoning to figure out more information about Δ ABC and its bisector !