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Presentation transcript:

Vocabulary Truths About Triangles MidsegmentsInequalities Relationships In Triangles

A segment whose endpoints are at the vertex of a triangle and the midpoint of the side opposite is a… Vocabulary 100

Median

A perpendicular segment from a vertex to the line containing the side opposite the vertex is called a(n)… Vocabulary 200

Altitude

A point where three lines intersects is called a(n)… Vocabulary 300

Point of Concurrence

Vocabulary 400 The point of concurrency of the angle bisectors of a triangle is called the…

Vocabulary 400 Incenter

Vocabulary 500 The point of concurrency of the altitudes of a triangle is called the…

Vocabulary 500 Orthocenter

The largest angle of a triangle is across from the _________ side. Truths About Triangles 100

Longest Truths About Triangles 100

Truths About Triangles 200 Given points and does point C lie on the perpendicular bisector of segment AB?

Truths About Triangles 200 Since AC = BC, point C is on the perpendicular bisector because of the perpendicular bisector theorem – point C is equidistant from the endpoints of the segment AB.

Truths About Triangles 300 The vertices of a triangle lie at, and Find the center of a circle that would be circumscribed about this triangle.

Truths About Triangles 300

Truths About Triangles 400 Given and find the coordinates of the midsegment that is parallel to BC.

Truths About Triangles 400

, and are vertices of triangle PQR.  What are the coordinates of T if is a median of the triangle?  What is the slope of if is the altitude from P?  Tell why or why not is a perpendicular bisector. Truths About Triangles 500

 T is the midpoint of , so find the slope of, and take the opposite reciprocal:  Midpoint of Truths About Triangles 500 is the perpendicular bisector

Midsegments 100 Find the value of x.

Midsegments 100

Midsegments 200 Find the value of x.

Midsegments ° Equilateral Triangle 5 5

Midsegments 300 Find the lengths of AC,CB, and AB.

6 7 5 Midsegments 300

Midsegments 400 Find the values of x and y.

Midsegments 400

Midsegments 500 Marita is designing a kite. The kites diagonals are to measure 64 cm and 90 cm. She will use ribbon to connect the midpoints of its sides that form a pretty rectangle inside the kite. How much ribbon will Marita need to make the rectangle connecting the midpoints?

Midsegments 500 The red segments are midsegments of the diagonal that measures 64 cm, so they measure 32 cm. The green segments are midsegments of the diagonal that measure 90 cm, so they measure 45 cm. So the perimeter is

Inequalities 100 Name the smallest angle in this triangle

Angle B Inequalities 100

Inequalities 200 Two sides of a triangle have measure of 12 meters and 22 meters what are the possible measures of the 3 rd side?

Inequalities 200

Can a triangle have lengths of 2 yards, 9 yards, and 15 yards? Inequalities 300

No!

If KM = 10, LK = 9 and ML = 18, find the order of the angles from smallest to largest. Inequalities 400

Angle M, Angle L, Angle K

If KL = x – 4, LM = x + 4 and KM = 2x – 1, and the perimeter of the triangle is 27, find the order of the angles from smallest to largest. Inequalities 500

If a point lies on the perpendicular bisector of a segment, what holds true about its distance from the endpoints of the segment? Relationships in Triangles 100

The point is equidistant from the endpoints of the segment. Relationships in Triangles 100

Solve for x. Relationships in Triangles 200

Point C is the centroid of triangle DEF. If GF, G being the midpoint of segment DE, is 9 meters long, what is the length of CF? Relationships in Triangles 300

Find the slope of the altitude drawn from vertex A. Relationships in Triangles 400

Find the slope of BC. The slope of the altitude drawn from vertex A will have a slope that is the opposite reciprocal of the slope of BC. So the slope of the altitude drawn from vertex A is 2.

Find the equation of the line that is the perpendicular bisector of segment CA. Relationships in Triangles 500

Step 1: Find the midpoint of CA. Step 2: Find the slope of CA. Step 3: The slope of the perpendicular bisector of CA is the opposite reciprocal of the slope of CA. So the slope of the perpendicular bisector equals. Step 4: Write the equation using point-slope form. Therefore the answer is: