Lesson 6-5 RightTriangles. Ohio Content Standards:

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Presentation transcript:

Lesson 6-5 RightTriangles

Ohio Content Standards:

Formally define geometric figures.

Ohio Content Standards: Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

Ohio Content Standards: Use right triangle trigonometric relationships to determine lengths and angle measures.

Ohio Content Standards: Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.

Hypotenuse

In a right triangle, the side opposite the right angle.

Legs

The two sides that form the right angle.

Legs Hypotenuse

Theorem 6-6 LL Theorem

If two legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent.

Theorem 6-7 HA Theorem

If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding angle of another right triangle, then the triangles are congruent.

Theorem 6-8 LA Theorem

If one leg and an acute angle of a right triangle are congruent to the corresponding leg and angle of another right triangle, then the triangles are congruent.

Postulate 6-1 HL Postulate

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another triangle, then the triangles are congruent.

Determine whether each pair of right triangles is congruent by LL, HA, LA, or HL. If it is not possible to prove that they are congruent, write not possible.

F D E G

Assignment: Pgs all, all