a + b + c = 180 Example: 1. a = 2. b = 3. a = 4.1 Interior angles of a triangle. a = 180 So a = 1 3. Find the missing measurements.

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1 4.1 Interior angles of a triangle. b a a + b + c = 180 c Example: a Find the missing measurements. a = 180 So a = a = 2. b = a b 3. a = 135 Triangle Sum onjecture: The sum of the measures of the angles in every triangle is 180 degrees. Here is why: a In a right triangle the two acute angles are angles. raw a triangle and think about the answer. 1

2 4.2 Properties of an Isosceles Triangle. Two sides of the same length Use your ruler, compass and protractor to confirm the following and mark the picture accordingly. a) Two sides are equal in measure. Vertex angle b) Two angles are congruent. Properties of an Equilateral Triangle. ll sides of the same length Use your ruler, compass and protractor to confirm the following and mark the picture accordingly. a) Three sides are equal in measure. b) Three angles are congruent 1. d=, e =, f = 2. j =, k =, l = f d e j k l 1 4 c m 6 f t 3. the perimeter of trangle N is 555m. Find the lenth of side N. N 2x+90 x

3 4. onstruct an isosceles triangle and then an equilateral triangle with only a compass and straight edge. Use the back of the previous page. 5. onstruct an isosceles triangle with a vertex angle that measures 30 degrees. 3

4 4.3 Triangle Inequalities Using your compass and a straight edge construct a triangle using the following lines: Using your compass and a straight edge construct a triangle using the following lines(if not possible then state why):

5 Measure the lengths of the sides of each triangle Triangle Inequality onjecture The sum of the lengths of any two sides of a triangle is than the length of the third side. *n extension of the Triangle Inequality onjecture: It is only possible to draw a triangle with three sides, if the sum of the shortest sides is than the longest side Is it possible to draw a triangle with sides of the given lengths? nswer yes or no. 4. 3, 4, , 7, , 5, 9 1. Side-ngle Inequality onjecture In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side rrange the letters values in order from greatest to least c 6 0 a b 2 5 a b c f t a 3 f t c b 2 f t 5

6 2. Triangle Exterior ngle onjecture The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. y x p Why is this true? 7. x + y= y 8. a= a x and 4.5 TRINGLE ONGRUENE ONJETURES. Ways to show two Triangles are ongruent: Side-Side-Side Side-Side-ngle Side-ngle-ngle ngle-ngle-ngle ngle-side-ngle Side-ngle-Side

7 onstruct a triangle, more than one if possible, using the following: a) b) c) raw a triangle with the following interior angles 45, 45, 90. Why did SS not work? Why did not work? 7

8 Mark the following triangles given the stated congruent triangle conjecture. Δ ΔEF SSS S E E F F S E SS E F F etermine which triangles are congruent and why? Using your previous conjectures mark congruent angles and sides if they exist and then find the corresponding congruent triangle. State the reason the two triangles are congruent.

9 1 OHW Which conjecture supports the congruence statement?(if not enough info, write not enough info) 2. s // s ( hint: transversal?), s s, There is not enough info here, why? 3. s s, s s, Which conjecture supports the congruence statement? E 9

10 5. sq s, squ su If you construct segment U, you can show QU U. Which conjecture tells you they are congruent? Q U 6. s s, Which conjecture tells you that? E

11 10. which conjecture supports each congruence statement? HF F H HGF EF 11

12 4.6 PT 1.. Which conjecture supports the congruence statement? ecause of both triangles are congruent. Which means s s,, and PT orresponding Parts of ongruent Triangles are ongruent 2. Which conjecture supports the congruence statement? E ecause of both triangles are congruent. Which means s se, s s,, and E 3. s s, s s, E s,, Which conjecture supports the congruence statement? (remember to split the triangles) E ecause of both triangles are congruent. Which sides and angles are congruent?

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14 4.7 FLOWHRT THINKING 1. Provide each missing reason or statement in the flow-chart proof. Given: Show: shr sse R S shu seu S Flow-chart Proof: E U H R 5. From the picture fill in the given and Prove: O K GIVEN O K GIVEN

15 6. Find the two congruent triangles and draw them next to each other, then write a proof. Given: Prove: spr spq spt sps PRT PQS GIVEN GIVEN 7. From the picture fill in the given and Prove: sow syw GIVEN GIVEN 8. Given: se se Prove: se se GIVEN GIVEN 15

17 4.8 More Properties of an Isosceles Triangle. Two sides of the same length Use your ruler, compass and protractor to confirm the following and mark the picture accordingly. a) Two sides are equal in measure. b) Two angles are congruent c) The bisector of the vertex angle is the altitude and the median to the base Vertex ngle Leg Leg ase ngle ase ngle ase 1. The following triangles are isosceles. a) = b) = c) =

H.Geometry Chapter 4 Definition Sheet

H.Geometry Chapter 4 Definition Sheet Section 4.1 Triangle Sum Theorem The sum of the measure of the angles in a triangle is Conclusions Justification Third Angle Theorem If two angles in one triangle are to two angles in another triangle,