Essential Question #1 Is it possible to have two right angles as exterior angles of a triangle? Why or why not?
Triangles are classified into two categories: Triangles Sides Angles Scalene Equilateral Acute Equiangular Isosceles Right Obtuse
(by sides) Scalene A triangle with no equal sides Isosceles A triangle with 2 equal sides Equilateral A triangle with all equal sides
(by angles) Acute A triangle with all angles less than 90 Right A triangle with one 90 angle Obtuse A triangle with one angle greater than 90 Equiangular A triangle with all equal angles
Legs The congruent sides Vertex Angle formed by the congruent sides Base Side opposite the vertex Base Angles Formed by the base and one of the congruent sides
If two sides of a triangle are congruent (legs), then the two angles opposite those sides (base angles) are congruent. If two angles of a triangle are congruent (base angles), then the two sides opposite those angles (legs) are congruent.
Triangle RST is an isosceles triangle. R is the vertex angle, RS = x + 7, ST = x 1, and RT = 3x 5. Find x and the length of each side. S R T
Given DAR with vertices D(2,6), A(4,-5), and R (-3,0). Determine type of triangle it is based on its side lengths.
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The sum of the measures of the angles of a triangle is 180 74 21 85
Find the measure of each numbered angle in the figure is AB CD. A 5 2 60 B 135 C 1 3 4 D
2 1 3 4 Given: ΔABC Prove: m 4 = m 1 + m 2
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Remote Interior Angle 2 Exterior Angle 1 3 4
Find the measure of each numbered angle. 65 82 46 1 3 2 4 142 5
Worksheet 4-2 Homework: Page 226 #30-32
Essential Question #2 Explain why you cannot prove that two triangles are congruent using 3 angles.
Are the following triangles congruent? Why or why not? M R 85 74 21 T S 74 21 Write a congruence statement for the triangles. L 85 N
Write a congruence statement for the set of triangles.
DO YOU NEED TO HAVE ALL SIX CONGRUENT PARTS IN ORDER TO DETERMINE IF TWO TRIANGLES ARE CONGRUENT?
1. Side-Side-Side Postulate (SSS) 2. Side-Angle-Side Postulate (SAS) 3. Angle-Side-Angle Postulate (ASA) 4. Angle-Angle-Side Theorem (AAS)
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.
Determine whether the triangles are congruent. If they are indicate the congruence postulate.
Given ΔSTU with vertices S(0,5), T(0,0), and U(-2,0) and ΔXYZ with vertices X(4,8), Y(4,3), and Z(6,3). Determine if ΔSTY ΔXYZ.
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Given: C is the midpoint of BF AC CE Prove: ΔABC ΔEFC Statements Reasons
Given: AB ll DE C is the midpoint of BD Prove: ΔCBA ΔCDE Statements Reasons
Given: BD bisects CDA CD DA Prove: ΔBCD ΔBAD Statements Reasons
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If two triangles are congruent, then all of their corresponding parts are congruent. In a proof, you MUST show that triangles are congruent, before you can show their parts are congruent.
Given: 2 1 4 5 Prove: BC DC Statements Reasons
Given: 1 4 Prove: DE EF Statements Reasons
Page 210 #29, 30, 33, 34
Essential Question #2 Compare and contrast the tests of triangle congruence (SAS, AAS, ASA) and the tests for right triangle congruence (LL, HA, LA).
A wind-surfing sail has 2 right triangles for the sailboard. In order for the sail to function properly, the two sails must be the same size and shape. Suppose that ΔDEF and ΔRST model the sails. What would be required to prove the triangles are congruent using SAS? D R E F S T
If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.
Triangle Proofs SAS AAS ASA/AAS D Right Triangles LL HA LA R E F S T
If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another triangle, then the two triangles are congruent.
If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.
If the hypotenuse and the leg of one right triangles are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
State the additional information, if any, that is needed to show that the triangles are congruent by the given postulate or theorem.
Find the values of x and y that make the triangles congruent.
Given: AB bisects CAD C and D are right angles Prove: BC BD
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