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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 If line DB is the perpendicular bisector of triangle DOG, find the value of x and y given: DO = 5x +15, DG = y + 4, D O G B

Truths About Triangles 200

Truths About Triangles 300 Find the equation of the median from A to in if the coordinates of the vertices are:

Truths About Triangles 300

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

Truths About Triangles 400

, and are vertices of triangle PQR.  If A is a midpoint, Tell why or why not  is a perpendicular bisector. Truths About Triangles 500

 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. Then find the perimeter of triangle ABC.

6 7 5 Midsegments 300 Perimeter = 18

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 Find the slope through the points (2a, -b) and (-7a, -2b)

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 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 400

Describe the Exterior Angle Inequality Theorem based on the diagram below. Inequalities

The measure of an exterior angle of a triangle is greater than each of its remote interior angles.

If a point lies on the perpendicular bisector of a segment, then it is _________ from the endpoints of the segment. Relationships in Triangles 100

equidistant 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 D G E F C GF = 9

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: Solve for b.