Lesson 6-5Lesson 6-5Right Right TrianglesTriangles

Ohio Content Standards:

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

Hypotenuse

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

Legs

Legs

The two sides that form the right angle.

Legs

Hypotenuse

Theorem 6-6 LL Theorem

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

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

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

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 Determine whether each pair of right triangles is congruent by LL, HA, LA, or triangles is congruent by LL, HA, LA, or

HL. If it is not possible to prove that they HL. If it is not possible to prove that they are congruent, write not possible.are congruent, write not possible.

Determine whether each pair of right Determine whether each pair of right triangles is congruent by LL, HA, LA, or triangles is congruent by LL, HA, LA, or

HL. If it is not possible to prove that they HL. If it is not possible to prove that they are congruent, write not possible.are congruent, write not possible.

F

D

E

G

Determine whether each pair of right Determine whether each pair of right triangles is congruent by LL, HA, LA, or triangles is congruent by LL, HA, LA, or

HL. If it is not possible to prove that they HL. If it is not possible to prove that they are congruent, write not possible.are congruent, write not possible.

Determine whether each pair of right Determine whether each pair of right triangles is congruent by LL, HA, LA, or triangles is congruent by LL, HA, LA, or

HL. If it is not possible to prove that they HL. If it is not possible to prove that they are congruent, write not possible.are congruent, write not possible.

Assignment:Assignment:

Pgs. 254-255 Pgs. 254-255 7-19 all, 7-19 all, 23-25 all23-25 all