* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download geometry chap 4
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Multilateration wikipedia , lookup
Golden ratio wikipedia , lookup
Euler angles wikipedia , lookup
Apollonian network wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Euclidean geometry wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Transcript
Acute triangle: the acute triangles has three acute angles that’s why it is called acute triangle. Equiangular triangle: the equiangular triangle has three congruent acute angles. Right triangle: the right triangle has one angle that makes 90 degrease and sense we know that this type of angles are called right angles these type of triangle gets its name from it. Obtuse triangle: these triangle has one angle of 180 degrease and the 180 degrease angles are called obtuse that’s why the triangle is called obtuse. Equilateral triangle: these type of triangle has three congruent sides. Scalene triangle: these triangle has no congruent sides. Isosceles triangle: at lear 2 congruent sides. Equiangular Right triangle Equilateral triangel Triangle sum theorem: the sum of the angle measures of a triangle is 180. Parts of a triangle: Interior: the interior of triangle is the set of all points inside the figure. Exterior: the exterior on a triangle is totally the opposite of the interior the exterior is the set of all points outside the figure. Interior angle: the interior angle of a triangle is formed by two sides of a triangle. Exterior angle: the exterior angle of a triangle is formed by one side of the triangle and the extension od an adjacent side. A K 45° C 60° 60° 90° B M<ABC +M<ACB +M<CBA=180° M<ABC +M<ACB=120° 180°-120°=60° 60+60+60=180° D M N m<kMN+m<MNK+m<NKM=180° m<kMN+m<NKM=135° 180-135=45° 45+45+90=180° M<DEF+m<EFD+m<FDE=180° M<DEF+m<EFD=110° 180-110=70° 70+55+55=180° E 55° 55° F The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. J 7x H K Find m<J H M<J +m<H=m<FGH (6x-1)° 5x+17+6x-1=126 11X+16=126 11X=110 126° X=10 (6x-1)° J F G M<J=5x+17=5(10)+17=67° (5x+17)° Find m<L L M<L+M<K=m<HJL 6x-1+7x=90 13x-1=90 13x=89 X=6.84 m<L=6x-1=6(6.84)-1 40.04 N (2y+2)° M 48° P Q find m<m M<m+m<N=m<NPQ 3y+1+2y+2=48 5y+3=48 5y=45 Y=9 M<m=3y+1=3(9)+1 M<m=28° Cpctc is a abbreviation for corresponding parts of congruent triangles are congruent these is proof that you may use. You may use these proof when triangle are on a coordinate plane. You use the distance formula to find the lengths od the sides of each triangle. Then, after showing that the triangles are congruent, you can make conclusions about their corresponding parts. K J reasons statements G H L 1. JL and HK bisect each other 2. JG congruent LG and HG congruent KG 3. <JGH congruent LGK 4. ▲JHG congruent ▲LKG 5. <JHG congruent <LKG 1. 2. 3. 4. 5. Given def. of bisect Vert. <s thm. SAS CPCTC A B D C 1. 2. 3. 4. 5. AB congruent to DC <ABC congruent to <DCB BC congruent to CB ▲ABC congruent ▲DCB <A congruent <D 1. EG congruent to DF 2. EG II DF 3. <EGD congruent to <FDG 4. GD congruent DG 5. ▲EGD congruent ▲FDG 6. <EDG congruent <FGD 7. ED II GF 1. Given 2. Given 3. reflex. Prop. Of congruency 4. SAS 5. CPCTC 1. 2. 3. 4. Given Given Alt. int. <s thm. Reflex. Prop. Of congruency 5. SAS 6. CPCTC 7. converse of alt. int <s Thm SSS: SSS is the abbreviation for side side side and these postulate says that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. SAS: SAS is the abbreviation for side angle side and these postulate says that if two sides and the included angle of one triangle are congruent to two sides and the included angle od another triangle, then the triangles are congruent. ASA: ASA is the abbreviation for angle side angle, the postulates says if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. ASS: ASS is the abbreviation for angle angle side and these theorem says that if two angle and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side od another triangle, then the triangles are congruent.