#Properties of parallel lines gsp5 series#

HS.G-CO (Congruence) Prove geometric theorems.

Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

Use geometric models to gain insights into, and answer questions in, other areas of mathematics.

Use visualization, spatial reasoning, and geometric modeling to solve problems:.

Use trigonometric relationships to determine lengths and angle measures.

Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.

Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.

Analyze properties and determine attributes of two- and three-dimensional objects.

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:.

Also, in this standard, students will study circles and their properties, with special focus on their applications. They will look at quadrilaterals and put them into a hierarchy, with 'special' quadrilaterals being 'nested' within others. They will work with scale factors in 'real-life' applications of similar figures. Students will study similarity and understand that congruence is a special case of similarity. They will see many types of triangles, including 'special' triangles such as isosceles, equilateral, right, 30-60-90 and 45-45-90 triangles, focusing on the properties of each of these figures. They will study angles formed by the three lines, and determine whether or not the two intersected lines are parallel. In this standard, students will work with a transversal that intersects two lines. The focus of this standard is on geometric figures, with the others listed above also being involved to a great extent. clarkii infected with WSSV.The study of geometric figures might be considered one of the 'main topics' in geometry, along with, among others, proportional thinking, reasoning and sense making. Therefore, the results presented in this paper provide new insights into the immune response of P. clarkii by inhibiting haemocytes apoptosis. These results indicate that PcVDAC promotes the replication of WSSV in P. In addition, after RNAi, the apoptosis rate was significantly increased (P < 0.05), the mitochondrial membrane potential was reduced ( P < 0.01), and the expression of caspase-3 and other genes was upregulated ( P < 0.05). The results showed that the number of WSSV copies in haemocytes was significantly reduced after RNAi ( P < 0.05), and the survival rate was significantly increased. The RNA interference (RNAi) method was used to explore the role of PcVDAC in WSSV infection. PcVDAC was expressed in all tissues tested, and its expression was upregulated after white spot syndrome virus (WSSV) infection ( P < 0.05). The gene was found to have a total length of 2277 bp, including a 194-bp 5′-UTR, 1234-bp 3′-UTR and 849-bp open reading frame (ORF), and to encode 282 amino acids.

clarkii ( PcVDAC) was cloned by rapid amplification of cDNA ends (RACE) technology. However, the role of VDAC in apoptosis and immune regulation in Procambarus clarkii is poorly understood.

Among apoptotic proteins, the voltage-dependent anion channel protein (VDAC) plays a key role in the mitochondrial apoptosis pathway because of its close connection with changes in mitochondrial membrane potential.

#Properties of parallel lines gsp5 series#

Apoptosis is programmed cell death that is strictly regulated by a series of related genes and is of great importance in resisting pathogen invasion and maintaining cell environment homeostasis.