1 / 10

Journal chapter 4 geometry

Journal chapter 4 geometry . By : Alejandro Hernández . Different type of triangles. 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.

ikia
Download Presentation

Journal chapter 4 geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Journal chapter 4 geometry By: Alejandro Hernández

  2. Different type of triangles 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. Isoscelestriangle: at lear 2 congruentsides.

  3. Examples of different type Of triangles Equiangular Righttriangle Equilateraltriangel

  4. Parts of a triangle and angle Sum theorem 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.

  5. Example of triangle sum theorem A K 45° 60° 60° 90° B C N M M<ABC +M<ACB +M<CBA=180° M<ABC +M<ACB=120° 180°-120°=60° 60+60+60=180° m<kMN+m<MNK+m<NKM=180° m<kMN+m<NKM=135° 180-135=45° 45+45+90=180° D M<DEF+m<EFD+m<FDE=180° M<DEF+m<EFD=110° 180-110=70° 70+55+55=180° 55° 55° F E

  6. Exterior angle theorem: 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 M<J +m<H=m<FGH 5x+17+6x-1=126 11X+16=126 11X=110 X=10 M<J=5x+17=5(10)+17=67° H (6x-1)° 126° (6x-1)° J F G (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

  7. Exterior angle example N 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° (2y+2)° (3y+1)° 48° M P Q

  8. CPCTC 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 JL and HK bisect each other JG congruent LG and HG congruent KG <JGH congruent LGK ▲JHG congruent ▲LKG <JHG congruent <LKG Given def. of bisect Vert. <s thm. SAS CPCTC G H L

  9. CPCTC examples D A AB congruent to DC <ABC congruent to <DCB BC congruent to CB ▲ABC congruent ▲DCB <A congruent <D Given Given reflex. Prop. Of congruency SAS CPCTC C B Given Given Alt. int. <s thm. Reflex. Prop. Of congruency SAS CPCTC converse of alt. int <s Thm 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

  10. SSS,SAS,ASA;ASS postulates SSS: SSS is the abbreviation for side sideside 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.

More Related