4.9 (M1) Prove Triangles Congruent by SAS & HL
-
Upload
chase-woodward -
Category
Documents
-
view
33 -
download
3
description
Transcript of 4.9 (M1) Prove Triangles Congruent by SAS & HL
4.9 (M1) Prove 4.9 (M1) Prove Triangles Congruent Triangles Congruent
by SAS & HLby SAS & HL
VocabularyVocabulary
In a right triangle, the sides adjacent to In a right triangle, the sides adjacent to the right angle are the the right angle are the legs.legs.
The side opposite the right angle is the The side opposite the right angle is the hypotenusehypotenuse..
Side-Angle-Side (SAS) Congruence Side-Angle-Side (SAS) Congruence Postulate: Postulate: If two sides and the If two sides and the included angle of one triangle are included angle of one triangle are congruent to two sides and the congruent to two sides and the included angle of another triangle, the included angle of another triangle, the two triangles are congruent.two triangles are congruent.
Hypotenuse-Leg (HL) Hypotenuse-Leg (HL) Congruence Theorem – Congruence Theorem – If the If the hypotenuse and one leg of a right hypotenuse and one leg of a right triangle are congruent to they triangle are congruent to they hypotenuse and leg of another right hypotenuse and leg of another right triangle, the triangles are congruent.triangle, the triangles are congruent.
ANSWER Yes; HL Thm.
Tell whether the pair of triangles is congruent or not and why.
Daily Homework Quiz
For use after Lesson 4.4
Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.
1. ABE, CBD
ANSWER SAS Post.
Daily Homework Quiz
For use after Lesson 4.4
Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.
2. FGH, HJK
ANSWER HL Thm.
Daily Homework Quiz
For use after Lesson 4.4
State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate.
3. ST YZ, RS XY
ANSWER S Y.
EXAMPLE 1 Use the SAS Congruence Postulate
Write a proof.
GIVEN
PROVE
STATEMENTS REASONS
BC DA, BC AD
ABC CDA
1. Given1. BC DAS
Given2. 2. BC AD
3. BCA DAC 3. Alternate Interior Angles Theorem
A
4. 4. AC CA Reflexive Property of Congruence
S
5. ABC CDA 5. SAS Congruence Post.
EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem
Write a proof.
SOLUTION
Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram.
GIVEN WY XZ, WZ ZY, XY ZY
PROVE WYZ XZY
STATEMENTS REASONS
EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem
1. WY XZ 1. Given
4. 4. Definition of a right triangle
WYZ and XZY are right triangles.
L ZY YZ5. 5. Reflexive Property of Congruence
6. WYZ XZY 6. HL Congruence Theorem
3. 3. Definition of linesZ and Y are right angles
2. 2. WZ ZY, XY ZY Given