* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Slide 1
Survey
Document related concepts
List of regular polytopes and compounds wikipedia , lookup
Euler angles wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Tessellation wikipedia , lookup
Golden ratio wikipedia , lookup
Four color theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Apollonian network wikipedia , lookup
Euclidean geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Triangles are cool! What is a perpendicular bisector in a triangle? goes through the midpoint and is perpendicular to the side What do you call the intersection of the perpendicular bisectors? midpoints circumcenter What do you call the intersection of the medians in a triangle? centroid What is a median in a triangle? connects a vertex to the midpoint of the opposite side Are the circumcenter and centroid the same point? An altitude in a triangle goes through a vertex and is perpendicular to the opposite side. ALTITUDE vertex perpendicular The intersection of the three altitudes in a triangle is called the orthocenter. That’s a fun word! Where is the orthocenter in a triangle located? C Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter? A B What about this triangle? C Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter? A B And how about this one? Notice that two of the sides had to be extended so that an altitude could be drawn. A C Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter? B Where is the orthocenter of an acute triangle located? Inside the triangle Where is the orthocenter of an obtuse triangle located? Outside the triangle Where is the orthocenter of a right triangle located? On the right angle vertex White Note Card: altitude / orthocenter An altitude in a triangle goes through a vertex and is perpendicular to the opposite side. The intersection of the three altitudes of the sides of a triangle is the orthocenter of the triangle. orthocenter Location: acute triangle: inside obtuse triangle: outside right triangle: on right angle vertex AE is an altitude. What is true about the diagram? A AE BC Is E a midpoint? BEA and CEA are both right angles. Could E be a midpoint? B E C A special segment is drawn in each triangle. Identify each special segment. What is XW? X Z W Y MD is an altitude in ΔLMN. Find the value for each variable. M Find the value for a, c, n, and x. LN = 4x - 1 a c x+1 (n² - n)° x L D x+5 N Make a Venn diagram to compare perpendicular bisectors, medians, and altitudes. bisectors and Medians only Medians True of medians only Perpendicular bisectors True of bisectors only True for all three Medians and Altitudes only Altitudes and bisectors only True of altitudes only Altitudes Circumcenters, centroids, orthocenters some of the coolest words I’ve ever said!