Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… ·...
Transcript of Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… ·...
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Chapter 4 Congruent Triangles
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4.1 Apply Triangle Sum Properties
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A shape with ________________________________.
Triangle
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Scalene: _____________________________________
Isosceles:_____________________________________
Equilateral:___________________________________
Classify Triangles by SIDE:
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Acute:______________________________________
Right:______________________________________
Obtuse:_____________________________________
Equilateral:__________________________________
Classify Triangles by ANGLE:
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EX: Classify the triangles by sides and angles.
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Interior and Exterior Angles
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The _____________________________ in a triangle ____________________________________.
Triangle Sum Theorem
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EX: Find x. Then classify then classify the triangle by its angles.
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The measure of an ___________________________ of a triangle_________________ the _______________ two ________________________________________.
Exterior Angle Theorem
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EX: Solve for x. Then tell the value of the exterior angle.
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The _______________________ in a right triangle are ________________________________________.
Right Triangle Angles
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EX: Find the measures of the acute angles in the right triangle shown.
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EX:
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4.2 Apply Congruence and Triangles
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Have exactly the ________________________ and ___________________________.
Have congruent _______________________________ and congruent ________________________________
Congruent Figures
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EX: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
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Find the value of x and m<H.
EX:
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If ________________________ of one triangle are ____________________ to ______________________ in another triangle, then the _____________________ are also _______________________.
Third Angles Theorem
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EX: Find the value of <B and <Z.
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EX: What is the m<DCN?
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4.3 Relate Transformations and
Congruence
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A ____________________ or __________________ in a figure to produce a __________________________.
Transformations
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A transformation that keeps __________________, ___________________, and _______________ the same.
Translations:
Rigid Motion
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Reflections:
Rotations:
Rigid Motion Continued:
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EX: Describe the transformation(s) you can
use to move the blue figure onto the red figure.
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4.4 Prove Triangles Congruent by SSS
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If __________________________ of one triangle are __________________ to ________________________ of a second triangle, the two triangles are ________________________.
Side-Side-Side (SSS) Congruence Postulate
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EX: Decide whether the congruence statement is true. Explain.
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EX:
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![Page 34: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/34.jpg)
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4.5 Prove Triangles Congruent by SAS
and HL
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If ________________ and the ____________________ of one triangle are _________________ to __________________ and the ___________________ of another triangle, then the two triangles are ________________.
Side-Angle-Side (SAS) Congruence Postulate
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EX:
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EX:
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EX: Decide whether enough information is given to prove that the triangles are
congruent by SAS.
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EX:
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Legs – the __________________________ to the ______________________
Hypotenuse – the side ________________________ of the ___________________________
Right Triangles
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If the ______________________ and a ____________ of a right triangle are ______________________ to the _____________________ and _____________ of another right triangle, then the two triangles are _______________________.
Hypotenuse-Leg Theorem
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EX:
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EX: Decide whether enough information is given to prove that the triangles are congruent. Is so, state
the postulate or theorem used.
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Prove Triangles Congruent by ASA and AAS
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If ____________________________ and the ________________________ of one triangle are congruent to ____________________________ and the _________________________ of another triangle, then the two triangles are ______________________.
Angle-Side-Angle (ASA) Congruence Postulate
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If ________________________ and a _______________________________ of one triangle are ______________________ to _____________ __________________ and a _____________________ of another triangle, then the two triangles are _____________________.
Angle-Angle-Side (AAS) Congruence Postulate
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EX: Is it possible to prove that the triangles are congruent? If so, state the
postulate or theorem used.
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EX: Tell whether you can use the given information to determine whether
________________
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All Triangles
Triangle Congruence Summary
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Right Triangles
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4.8 Use Isosceles and Equilateral
Triangles
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Isosceles Triangles have ________________________
Parts of Isosceles Triangles:
Isosceles Triangles
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If _____________________ of a triangle are congruent, then the ___________________________ are _____________________.
Base Angles Theorem
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If ___________________ in a triangle are congruent, then the __________________________________ are ___________________.
Converse to Base Angle Theorem
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If the measure of vertex angle of an isosceles triangle is 112°, what are the measures of the base angles?
EX:
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EX: Solve for x.
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EX: Find the value of x and y.
![Page 61: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/61.jpg)
Equilateral Triangles have _______________________
Equiangular Triangles have ______________________
All ____________________ are also _______________
All ____________________ are also _______________
Meaning:
Equilateral and Equiangular Triangles
![Page 62: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/62.jpg)
EX:
![Page 63: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/63.jpg)
EX:
![Page 64: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/64.jpg)
EX:
![Page 65: Chapter 4 Congruent Trianglesmrsmyersmath.weebly.com/uploads/1/3/3/0/13301533/geometry_chapt… · 4.2 Apply Congruence and Triangles ... Write a congruence statement for the triangles.](https://reader036.fdocuments.us/reader036/viewer/2022062318/5ffced4cb7e737691c0ab9e5/html5/thumbnails/65.jpg)
EX: