formal geometry
TRANSCRIPT
Formal Geometry Unit 4 β Congruent Triangles
Section 4.1 β Angles Triangles Classifying Triangles by Angles
Acute Triangle-
Obtuse Triangle-
Right Triangle-
Equiangular triangle- Classifying Triangles by Sides
Scalene Triangle-
Isosceles Triangle-
Equilateral Triangle- Examples 1-3: Classify each triangle as acute, equiangular, obtuse, or right.
1. βπ΄π΅π· 2. βπ΅π·πΆ 3. βπ΄π΅πΆ
Examples 4-5: πͺ is the midpoint of π©π«Μ Μ Μ Μ Μ and point π¬ is the midpoint of π«πΜ Μ Μ Μ Μ . Classify each triangle as isosceles, scalene, or equilateral.
4. βπ΄π΅π· 5. βπ΄π΅πΆ
Example 6-8: Find π and the measures of the unkown sides of the triangle. 6.
7. βπΉπ»πΊ is an equilateral triangle with πΉπ» = 6π₯ + 1, πΉπΊ = 3π₯ + 10 and π»πΊ = 9π₯ β 8
8. βπππ is an isosceles triangle with ππΜ Μ Μ Μ Μ β ππΜ Μ Μ Μ . ππ is two less than five times π₯, ππ is seven more
than two times π₯, and ππ is two more than three times π₯.
Theorem List
Theorem 4.1- Definitions
Exterior angles-
Remote interior angles-
Theorem List
Theorem 4.2- Corollary-
Corollary 4.1-
Corollary 4.2- Examples 9-10: Find the measure of each numbered angle. 9. 10. Examples 11-12: Find each measure.
11. πβ 1 12. πβ 3
Section 4.2 β Congruent Triangles Definitions
Congruent Polygons-
Corresponding parts- Theorem List
Theorem 4.3-
Theorem 4.4-
Properties of Triangle Congruence
Example 1: Find π and π. 1.
Example 2: Draw and label a figure to represent the congruent triangles. Then find π
and π.
2. βπ½πΎπΏ β βπππ, π½πΎ = 12, πΏπ½ = 5, ππ = 2π₯ β 3,πβ πΎ = 67,πβ πΏ = π¦ + 4, and πβ π = 2π¦ β 15 Example 3: Write a 2 Column Proof Given: β π΄ β β π·
Prove: β π΅ β β πΈ
Section 4.3/4.4 Day 1β Proving Congruent Triangles Postulate List
Postulate 4.1-
Postulate 4.2-
Postulate 4.3- Theorem List
Theorem 4.5-
Proving Triangles Congruent
SSS SAS ASA AAS
Examples 1-4: Determine which postulate can be use to prove that the triangles are congruent. If it is not possible prove congruence, write not possible. 1. 2. 3. 4. Example 5: Write a congruence statement for each pair of triangles represented:
5. πΉπ΄Μ Μ Μ Μ β π»πΜ Μ Μ Μ , π΄πΜ Μ Μ Μ β ππΊΜ Μ Μ Μ β π΄ β β π Examples 6-7: Determine whether each pair of triangles is congruent. If so, write the congruence statement and why the triangles are congruent. 6. 7.
Examples 8-9: State the 3rd congruence that must be given to prove that the Ξ' ares ,
using the indicated method. (what other corresponding parts are needed) 8. Method: SAS 9. Given: πΆπΜ Μ Μ Μ β π·πΊΜ Μ Μ Μ πΆπ΄Μ Μ Μ Μ β π·πΜ Μ Μ Μ
Method: SAS
Section 4.3/4.4 Day 2β Proving Congruent Triangles 1. Given: π πΜ Μ Μ Μ β₯ ππΜ Μ Μ Μ Μ ππΜ Μ Μ Μ Μ β ππΜ Μ Μ Μ
Prove: βππ π β βππ π
2. Given: ππββββ βπππ πππ‘π β πππ΅
ππββββ β πππ πππ‘π β πππ΅
Prove: βπππ β βπ΅ππ
3. Given: πΈπ΄Μ Μ Μ Μ β₯ π·π΅Μ Μ Μ Μ πΈπ΄Μ Μ Μ Μ β π·π΅Μ Μ Μ Μ
π΅ is the midpoint of π΄πΆΜ Μ Μ Μ Prove: βπΈπ΄π΅ β βπ·π΅πΆ
Section 4.3/4.5 Day 3β No Notes
Section 4.4/4.5 Day 4β CPCTC CPCTC-
1. Given: β π»πΊπ½ β β πΎπ½πΊ β πΎπΊπ½ β β π»π½πΊ
Prove: π»πΊΜ Μ Μ Μ β πΎπ½Μ Μ Μ
2. Given: βπππ β βπππ β πππ β β ππ π
Prove: βπππ β βππ π
Section 4.5 Extension-HL Theorem Review In a right triangle the sides are called: Hypotenuse- Legs-
Theorem List
Theorem 4.9-
1. Given: β π΄π΅π· and β πΆπ΅π· are right β β²π π΄π·Μ Μ Μ Μ β πΆπ·Μ Μ Μ Μ
Prove: βπ΄π΅π· β β πΆπ΅π· 2. Given: β πΉπΊπ» is a right β
β π½π»πΊ is a right β πΉπΊΜ Μ Μ Μ β π½π»Μ Μ Μ Μ
Prove: βπΉπΊπ» β βπ½π»πΊ
3. Given: π΄π΅Μ Μ Μ Μ β₯ π΅πΆΜ Μ Μ Μ π·πΆΜ Μ Μ Μ β₯ π΅πΆΜ Μ Μ Μ π΄πΆΜ Μ Μ Μ β π΅π·Μ Μ Μ Μ
Prove: π΄π΅Μ Μ Μ Μ β π·πΆΜ Μ Μ Μ
Section 4.6 Isosceles and Equilateral Triangles Review: Isosceles triangle-
Legs-
Base-
Vertex angle-
Base angles- Theorem List
Theorem 4.10-
Theorem 4.11-
Corollaries:
Corollary 4.3-
Corollary 4.4- Examples 1-2: Find each measure. 1. πΉπ» 2. πβ ππ π Examples 3-4: Find the value of each variable. 3. 4.